The Terrans aren't as technologate as the mighty Protoss, or as instinctive as the gruesome Zerg, but when it comes to survival, Terrans beat all. They are best with resourses and robotics. Terrans are, by far, the most organized species.
The number one best strategy is to establish two or more bases to mine resourses and train units. When you do this, you can escape to one of your other bases with your mobile buildings and keep going without loosing any. Another great defense is to build bunkers and missile turrets around your base and put Marines, Firebats, and/or Ghosts. You also want Seige Tanks around your perimiter so you can get the first strike.(and also place spider mines everywhere.)
Terrans don't have much when it comes to defense, but their offense is astounding! Terrans are good with suprise attacks especialy when you have Ghosts or Wraiths.
A great attack is to come in with a lot of marines and/or firebats. After that, you attack with any cloaked units. If they still are alive, attack with heavy artillery such as, Battlecrusers and/or Seige Tanks.(this attack doesn't work with Zerg.)
Another great way is to start out destroying the outer defense with Nuclear Strikes and/or Seige Tanks. If you still have some Nuclear warheads or Seige Tanks still alive, keep attacking with a backup group. (this works great with attacking Zerg.)
Another attack is to attack from all around in big groups. First, start out attacking from behind or from the sides. Next, attack from the front as soon as some units die. Then, you attack from the remaining sides. (tip: always have backup units for every attack. That way, if all of your units die and they are weak from the attack, you could just bring them in.)
Terrans are also good at just brute force. Just come in with stuff from the factory and get Battlecrusers and just tear everything apart.
If you get stuck with cloaked units, just have Science Vessels in the attack area. If you get stuck by getting stuck by lockdowns, just have marines and/or firebats in the area. (remember, when fighting other Terrans, have marines and/or firebats following your mechanical units.)
When attacking Protoss, always have a Science Vessel around with EMP Shockwave so you can disable their shields. If the Protoss have Archons, always use the EMP Shockwave on them. Also, before any attack, you should scan the path and area you will be attacking at so you know what you should have.
When attacking Zerg, use the brute force strategy first and have the backup units right behind them so you don't give the Zerg time to regenerate.