The Basics
Seth is a very adaptable character. He has many tools at his disposal, including a fireball, a command grab, an uppercut, a teleport, and a good combo ender in Hyakuretsukyaku. Seth can either be played extremely defensive and patient, or extremely offensive and smothering to the opponent. The main sacrifices he makes for all of these tools are below average normals, terrible walk speed, and health. While it has slightly increased since his introduction in vanilla Street Fighter IV, Seth still crumbles once the opponent lands a good hit. With the nerfs to his Shoryuken, Tanden Engine, and stun output, many players find him less viable as a result.
Seth is not a lost cause in the slightest, however. Once he finds an opening and knocks the opponent down, the mixup game remains strong, even with the introduction of delayed wakeup. Keeping your opponent guessing is Seth's main gameplan, and he will win if all the dice rolls are in his favour. If the distance is kept, however, Seth still has the far limbs and fireballs to keep the opponent out and force them to come to him.
Strategy
"It's the battle of the century... Fight!"
At the start of a round, there are generally two things you can do; either back off and wait for them to act first, or dash up in their face to see how they react to your movement. The former is safer, but the latter can catch your opponent off guard. If you've never played your opponent before, however, it's probably best to stick to defensive gameplay for the first few seconds. A middle ground to these strategies would be to play footsies instead—which Seth CAN do—but his normals are not up to par with characters like Fei Long or even Ryu. He does have st. MP and st. MK as medium ranged normals, and cr. MP and cr. MK can be buffered into MK Hyakuretsukyaku. Do not use far st. HP at regular footsie range; it is very slow and easily punishable if they jump over it or focus through it. Even at full screen, it is still possible to whiff punish it or even counter hit it. Only use far st. HP at the tip of its range, where it can still hit but they are forced to either block it or try to preemptively counter hit it, which they need a hard read for. In any case, if you play your cards right, you will eventually end up knocking them down.
Mixup Opportunities
If you land a Hyakuretsukyaku mid-screen, you can either simply maintain the distance or teleport forward behind them or in front. Your options if you teleport forward are somewhat limited if they do quick wakeup, but at best, you have a slight frame advantage. In this case, you can either go straight into an SPD, Shoryuken (if you're really antsy), or simply wait out and see what your opponent does to collect data. If they don't do quick wakeup, you are basically free to do what you want; dive kick on top of them, cross them up with jump LK or MK (jump LK leads to a very good tick throw setup while jump MK can lead into another combo if it isn't blocked), empty jump SPD, or just crouch tech option select with cr. LP + cr. LK xx cr. LK + cr. MK; if they backdash, most characters will get caught and you can buffer an MK Hyakuretsukyaku. If they block, they are stuck blocking and you can SPD them if they are within range. If you manage to hit them, you can keep doing cr. LK chains or link into cr. MP with cr. LP if they are close enough. An added bonus if they don't quick wakeup is a side-to-side mixup using Sonic Boom FADC Teleport. In the corner, you can just do head stomps into dive kick and either stay in front or walk forward to cross up and hit them low as they fall back to the ground. Sometimes after the dive kick, you will end up behind them, and in some cases you can walk backward to keep the corner position, but most of the time, you'll have to dash back to get the right position; you can still mixup whether you'll hit them low or just SPD them as they fall.
If you're close to the corner but out of range for head stomps, you can set up a 4 frame safe jump if they quick wakeup after the Hyakuretsukyaku; just immediately jump and do a late dive kick. It'll keep you safe from any 4 frame reversal or slower and force them to block high. If they don't quick wakeup, you can stay still for a few frames and attempt another safe jump. More info here: USF4 - Seth safe jump set ups after Lightning Legs
Landing an SPD leaves you in a very good position. After the move ends, you can dash up, position yourself properly, and either do a jumping forward crossup mixup, empty jump crouch tech, or empty jump and do SPD again to keep them in this loop. Some characters can auto-correct and still hit you while you're in the air; in that case, just keep the mixup grounded and simple with either crouch tech or SPD. If you land this move in the corner, you don't really have to do much if you don't want to. Just make sure you keep them there.
The situation after a Shoryuken largely depends on whether they quick wakeup or not; if they do, you can dive kick right on top of them, cross them up with jump LK or MK, or empty jump SPD/crouch tech. If they don't quick wakeup, you are free to do any mixup you desire.
If you have a hard read on a backdash, you can simply use the Tanden Engine a little bit early to catch a backdash.
Landing Tanden Stream affords you one of the only feasible ways to do a Sonic Boom/Yoga Teleport mixup without spending two bars to FADC the Sonic Boom. Usually, the opponent will wake up with the Sonic Boom on top of them whether they do delayed wakeup or not, and this is a great round ender because most of the time, the opponent will not think to reversal the Sonic Boom.
On the Defensive
If you're in a situation where YOU get knocked down, you will have to carefully evaluate your options, since Seth has (arguably) too many options on his wakeup. The most obvious and probably riskiest one is his Shoryuken; it does knock your opponent down and can blow through any move with the proper timing, but if it gets blocked, Seth is left wide open for big damage combos. SPD is the middle ground for being fast and unblockable, but it's short ranged, and it will lose to jumps, backdashes, and meaty attacks (unless it's EX). Teleport is the safest option, but it can be option selected, and because it doesn't go very far, you can still be left open to a decent punish if your opponent has access to one. Seth also has a backdash that goes a fair distance, but that too can still be option selected. That just leaves blocking, crouch tech, stand tech, and jump away, something every character has access to. Even though Seth is tied for having the lowest health in the game, most Seth players are very reckless on defense, often jumping immediately to the first three options I mentioned right away, without accounting for the basic options, particularly blocking. A Seth player should not be afraid to block by any means, even if blocking eventually translates to 100 chip damage sustained. It's much better to eat that much chip than to succumb to frame traps or option selects that the opponent called you out for.
Ultra Selection
Tanden Stream is generally the preferred Ultra for most matchups because it is much more well rounded in usage, and it can punish from full screen like no other Ultra. There are some matchups that might require Tanden Typhoon, as Tanden Stream loses to moves that can stall in the air. Tanden Typhoon can also juggle from his moves relatively well and deal quite a bit of chip damage, but I personally evaluate Tanden Stream as too valuable to pass up, and so use Ultra Combo Double in those situations.