Start the game with a
. Then you go
AP and survivalbility all in one. Boots is optional, but I prefer more defensive boots like merc or tabi rather than the one with magic penetration, I also tend to NOT complete boots early (as in, leaving it as boot tier 1) because Swain is all about making the enemies come at you so there is no rush for higher MS.
Use Sorcery+Domination. For Sorcery do: Comet+ManaflowBand+Transcendence+either Scorch or GatheringStorm (I prefer Scorch because I start the game with Corrupting Potion). Domination you do: CheapShot+Ravenous Hunter.
Use E to poke opponent in lane, Q to farm unless you land a E which in the case you quickly do a pull->Q and go back to farming (that's where the Comet comes in, because it will land on the enemy's head most of the time given your E); use W to scout for potential ganks coming at you, though you can also use it on your lane opponent to help building your fragment stacks beyond just gaining it from pulls but it's a bit tricky to land (may be easier if you land E first). By repeating this you can bully most opponents out of lane. You don't really try to finish opponent before 6, unless a teammate is doing a gank for you or if the opponent is really suicidal, otherwise your aim is generally to bully them enough and when you get 6, you try a pull, if you do get it then use ulti to finish them off, preferably if there's minions for you to leech off.
Remember, your E is incredibly powerful as a continuous poke and zoning that can also be used to help you sustain in lane. Learn how to land it effectively and use it to bully your opponents. You can also move after throwing E out and the it will come back to you all the same, so you can do a "V" shape pull by walking sideways after tossing E, and it should catch most players.
Also unlike old Swain, you can still use normal spells during ulti, so remember to use your normal spells and not just walking around waiting for the charging blast. You also want to activate your R almost at the start of a fight, don't drag it out and wait for the last second.
Oh and, your pull works on all immobilisation from all ally sources, it doesn't have to be from your E. So keeps your eyes out.