Early game in TvP you want to open up with a depot, refinery rax build and then follow it up with a fast expansion. This is the safe and standard macro style which will allow you to get a reaper out early for some map presence as well as let your economy get online. Now there are some other options, for example, you could proxy a factory and then try to get some damage done with an early cyclone push because the cyclone is a very powerful ground unit. You can also do a fast cloaked banshee rush with a proxy starport, and in fact, you can also do that even if you do a fast expand, but the percentage play is to just open with the expansion right away and then go into your own early game strategy.
You are going to want to send your reaper across the map right away to maybe pick off a probe or two but more importantly get that crucial scouting information and find out what your opponent is planning. If you can get confirmation of either the starport or robotics facility that would be great because then you can make the right adaptations. If you do scout a stargate then you should expect an early oracle attack, possibly complemented by a few adepts as if the oracle is denied worker damage it can still jump on small groups of marines quite nicely and clear the way for the adepts to really get some work done. If you can’t get hard confirmation of either tech path you are definitely going to want to prepare for oracles because they are a very common opening and if you are caught off guard then it is game over. So this means a turret at one base and a widow mine at the other. Widow mines do one shot oracles and are very difficult to dodge unless you are a top-tier Korean player. If you want to get fancy you can opt for unorthodox widow mine placement in order to out level your opponent.
In terms of strong opening strategies for terran, you do have a lot of options. One really great build is to just do a simple 2-1-1, standing for two barracks, a factory, and a starport. The idea here is that you just pump out a lot of stimmed marines early on and go and do some damage before your opponent has a strong answer for marines like upgraded colossi. With any luck, you might be able to cancel your opponent’s third base and secure an economic advantage leading into the late-mid game.
Another option is the 1-1-1, which is basically just rushing up the tech tree as fast as possible so that you can get right away into the production of starport units such as medivacs or banshees. Cloaked banshees can be devastatingly effective during the early game if your opponent doesn’t have detection but they are a bit of a gamble because if you don’t do any damage then you will be a little behind and banshees do not scale well into the late game. If you are doing a 1-1-1 build you will want to swap out your reactor from your barracks so that your factory can do the double pump of hellions which are great for run-bys early on and will allow you to conserve your gas.
During the midgame, you will want to utilize the mobility of dropships to harass outlying expansions while building up a strong composition of marines, marauders, medivacs, tanks, and vikings. Vikings are going to be necessary in order to take out colossi which would otherwise just rip your infantry forces to shreds. It is crucial to hotkey your individual unit types for maximum effectiveness. While drops are a great way to get value out of a small number of units you also want to be careful about bleeding forces off too easily because small losses here or there can make the difference when you do have a massive engagement later on. Make sure to get the maximum utility out of your drops by keeping everything alive as long as possible and going back for seconds and thirds.
Queueing up liberators to siege up in defender mode on an opponent’s mineral line is a nice low apm method of accomplishing some mid-game harass and forcing your opponent to react to you. If you feel that you are in a good position army wise then you will want to move out and try to take out one of your opponent’s base. Choosing the right engagement is critical to your success here. You do want to be careful about your troops getting too bunched up because a lot of protoss players are opting to include psy storm in their death ball and you will want to be able to dodge most of the damage from this spell. Make sure to focus fire your vikings on the colossi and don’t run too far forward with these units because you don’t want them to get picked off by stalkers or archons. If you are in an all-out engagement then you should probably go for it but if your armies are sort of just standing apart then you don’t want to go too far forward and lose your viking count or you will have no answer to the colossi. You also have to be careful about making too many vikings, because after the colossi are taken out these guys are pretty worthless, although the landed vikings helping out in a battle is always a pretty epic sight.
Positioning your tanks correctly and making sure to include a decent amount of marauders in with your forces is very important. During the mid and late game liberators become a crucial component of the terran composition and by leap frogging your tanks and your liberators things become very difficult indeed for your protoss opponent.
Make sure to stay on top of your upgrades, both the attack and armor upgrades that make your combat units more powerful but also upgrades like advanced ballistics that give your liberators more range. The advanced ballistics upgrade is a total game changer during the mid and late game.
Late game TvP is all about cost efficiency and value. High tech units like ghosts and ravens become quite valuable as landing a few EMPs can completely negate the ability of templars to do damage and make the protoss units that much easier to kill. You will want to make sure that by this point you are producing off multiple factors and tanks so that you do end up with that higher tech unit composition and don’t rely quite as much on barracks production unless you end up in a massive engagement and need to remax as quickly as possible. Make sure that you keep up on expansions and keep putting pressure on your opponent’s undefended bases. During the extreme late game terran does have the opportunity of making multiple extra orbital command centers, which will allow you to not replace some scvs that die in run-buys or battles. These orbitals will also provide invaluable scouting information through the use of your scan.
You have to make sure that when you do fight you are trading out effectively or winning battles by positioning your units correctly and micromanaging your forces for maximum effectiveness. Try to maintain control over the center of the map whenever possible and you can even set up sensor towers at key locations to provide constant information about any attacks or drops that might occur in your territory.