Terran Offense
Terran offensives are a little more difficult to pull off than othe rraces. They don't have the brunt force of protoss nor do they have the sheer speed of zerg units. They have a lot of power in a little space...the problem is that it is slow. All terran units are slow as hell. Tanks siege slowly, they move slowly...the same goes for goliaths. That means you have to be prepared for a counterattack because there's hardly any chance that you can pull back your troops from your attack to save your base...by the time you get their, it'll be half dead. So always leave your barrack grounded (read above about choke point defense) when you're not moving units out of your base.
Keep about 4~5 tanks on your ridge sieged and make sure they're spread apart such that no more than one tank can be hit at a time by psi storm. When you get attacked, use your scvs to block all units from getting to your tanks. Target any templar you see and keep pumping troops. Never stop pumping troops. It hurts terran more than any other race. You always have to be pumping troops. Terran attacks are 40% timing, 40% position, 5% macro, 5% power, and 50% micro (that'd be 150%...I guess my math ain't too good...stfu, I know that wasn't funny). Just keep that in mind. Terran troops are not at all expendible. Losing your entire force will lose you the game. You can't rebuild your entire force within seconds like you can with zerg, nor defend yourself with a few units like protoss (templar and reaver). Keep that in mind.
Most people don't know how to tank push properly. They just slap all their tanks together and hope that enemy templar won't come close enough to psi storm. That's not the way to play. Always spread apart your tanks!!! I can't emphasize that more. When you siege your tanks, siege them individually and manually. Often, you can have them move to a spot in your enemy's base. As they get close, siege them one by one. Since you're not sieging them all at once, the ones you siege first will typically be at the back if you group and the once you siege last will be at the front of your group (I know that isn't always true wise ass...stfu). They will be spread apart just fine. It's ok if you have some of the tanks at the back of your group clustered because they most likely won't get stormed. However, just keep in mind that you never want your tanks clustered. Also, always have 4~5 vultures with every attack resources permitting. These buggers can take out templar in one volley. Don't rush in with those vultures as you see their goons coming. Once their troops have engaged your troops, send in the vultures. The vultures most likely won't be targetted for a few seconds, giving you time to take out all their templar.
What if they go dragoon contain? I made a little tip a while back on beating dragoon containment. Let me elaborate a little bit more on it. Dragoon containment is when they park a bunch of dragoons in front of your base with templar. Seemingly, this minimal force wouldn't be able to stop the big terran army, but because terran don't have the position (their siege tanks aren't sieged as protoss troops run in, but the tanks are sieging as the protoss troops come in), they don't have the time to separate siege tanks, and they're often caught at the choke point right in front of their base, it all spells doom for the terran player. You often don't want to face dragoon containment head-up as you can often lose many times more money than the protoss player does, and more often than not, your entire force. Rather than wasting your money on trying to penetrate their goon containment, or pushing all the way across the map, you can circumvent their entire force.
If you sense the goon containment early, or even if you don't, commence construction of dropships as soon as you get your starport. The protoss player usually plays by expanding to different plateaus early on while dragoon containing you. They do not expand to their natural until they have shuttles to deal with ridge drops from you. If they didn't dragoon contain, they would never have enough dragoons at all their bases to defeat a head-on attack from you when you have the positional advantage. That is why dragoon containment was made basically. Some protoss player found that it was very difficult for terran to deal with dragoons when the tanks were sieged prior to engagement.
Anyway, use dropships to deal with this. Dropping in a payload of tanks and goliaths will not only ensure the positional advantage, but surprise, and added bonus that can pay big dividends. 3 dropships is ideal early on. The ideal payload is 8 goliaths and 2 tanks. Just take out all the defense they have near their nexus (shouldn't be too much if they're dragoon containing you) and then destroy the nexus asap. EMPing the nexus really helps if you have it. Below is an animated GIF showing how to kill a protoss base quick. Lots of EMP and troops did the job in 30 seconds. It's a little more than you need, but I hope it gets the point across...

Click on the picture to see the animated GIF.
After they lose an expansion, I like to keep my forces there and take the expansion as my own...But I'll talk about expanding later. After your initial drop, they'll be thrown in chaos...if you destroyed their nexus that is (which you should have by all means). Just constantly drop different bases until they drop their goon contain or stop pumping reinforcements to their goon containment. Then, you can just attack them head-up. Just remember, it's all about timing. You may be wondering why I'm emphasizing goon contain so much. Goon contain is the strategy that protoss players employ on me when I'm terran 90% of the terran, Korean or American. If they don't goon contain you, you can attack them head-up, which I'm sure anyone reading this can do.
Now, I can't emphasize the importance of goliaths. They are great support units. They can easily dance out of storms without taking too much damage, they are carrier-killers (and shuttle killers), they have decent attack power, and they are cheap. As long as you constantly pump goliaths from two factories and tanks from the other two, you should maintain a good ratio. Also, when you're up against mass zealot/dt, keep your tanks unsieged for chrissake. I've seen people essentially kill half their own force with their own sieged tanks. If you encounter a mix of zealot/dragoon/dt, siege your tanks, but manually attack their dragoons. Zealots are only there to make you damage yourself. Your support should take care of any melee units easily. You have to manually target dragoons. They are the real damage dealers and the ones you want to deal damage to.
Also, you can use a decoy to really throw them off. Instead of overlords, use dropships of course. You want to use at least four to make it seem threatening enough for them to move their troops from their entrance. Once you feel like they have moved their goon contain, scout with a vulture to check if it's true. If they haven't budged, it's most likely because they knew your dropships weren't loaded and that they hack. (This is what happened...this guy who will remain nameless didn't do a thing about the dropships, although he obviously saw them...I didn't say anything about it until I shared vision with him for 2 minutes and he hadn't noticed. Anyway, back to strategy.) If the coast is clear, send out an attack on a different base from the one you sent your dropships too. They most likely will be caught with their pants down. I liked to siege up all my tanks in front of the base where their goons went to rescue and then have a couple of tanks and goliaths kill another base. The point is that dragoon contain will be temporarily dropped. This is the time to act. Remember, timing is everything.
Also, you can go marines. If you sense they're going heavy goon contain from the moment you expand, throw up two engine bays and 6 barracks. Just don't let them see your marines until the second you're ramming them down his arse. Also, have vultures to take out the templar. Suicide your vultures if you have to, because with psi storm or two, those marines can become a lot uglier than they already are. Then, after that, tank push him immediately. You can most likely kill an expansion with 12 marines, a couple of medics, and 2 tanks. Never stop pumping troops and get science vessels asap. The key to going marines is surprise. Once you take down their goon contain, as long as you don't act retarded, the game's all yours. Expand all over as soon as their goon contain is down and do whatever you want. I like to constantly pump marines and build battlecruisers, just like the vanilla days. But that's just a suggestion. Just remember that the point of going marines is to take down their dragoon containment. Constantly build vultures to take down their templar, some tanks to take care of reavers, and your marines can take care of anything else. I don't suggest going marines otherwise.
I'm sure everyone here knows how to pull off a ridge drop. I like to hold off my ridge drops until I have goliaths to deter shuttles and act as support. My suggested payload for ridge drops is 4 goliaths (or more...the more goliaths the merrier) and 2 tanks. Just have a set of 4 goliaths patrol each side of the ridge and have them act as support if any shuttle actually manages to drop their payload. Also, have comsat handy just in case they drop dts. Science vessels aren't that important against protoss (when going heavy metal) as long as you have good micro. They're usually only good for detection and EMPing structures. EMP on units is inaccurate and has a relatively small effect radius for the actual effect the spell has.
Don't worry about them. Spend your gas on troops. If you haven't noticed thus far, all these terran attacks are conservative quick-strikes that are intended to have a lot more output than input. Executing these attacks with proper timing is 80% of it. Timing is something I cannot write a strategy about. Just attack the base with the least defense and the most valuable structures. Whichever one you find more significant. Remember one thing. If they're not goon containing you, don't drop them. You're wasting your time dropping them. Hit them head-up.