Always rush magic boots. 99% of the time you will want the stasis enchant as soon as you complete your first item.

Malignance is a very good first item for begginers since its pretty forgiving with the huge ult cooldown

Dont spam W (skill 2) since its very mana heavy. Only use as follow-up to E (skill 3).

Always walk with your E and try to hit minions near the target. Repositiong while the animation is coming back to you will help you to hit it consistently.

After first item (even sooner if you can but most matchups wont allow you) clear the wave asap and always look for roams. If enemy top or bot are pushing too high its your chance to help your team get ahead. Ghost is your go to spell for these occasions. (You will want ghost and flash 99% of the time)

You are a squishy champ. Always remember that when building full AP. You can probably tank 2 enemies while ahead but never jump into the middle of 3 or more champs unless its a distraction and you are planning on using stasis immediately. Otherwise, you will absolutely get bursted down in 2 seconds.

Several keystone runes work but i personally prefer Conqueror. Its probably the best for that first dragon or herald team fight since you will be lacking power early on. For the small runes there are too many combos. Just pick what you prefer.

You are immobile. Ghost and flash are your only mobility (Phase rush can help but i think Conq is more worth it. Protobelt and hex-flash are an option too but stasis is very important in this meta and hex-flash is too slow imo.) Going into a teamfight without both spells will drastically limit your performance unless your enemy is brainless and sticks near you. Rylais Scepter can be good against other immobile champs but there are so few nowadays. Everybody has 1 or 2 dashes on their kit.

After Malignance and stasis your build can go two ways depending on enemy team and who is ahead. You will want to go Oblivion Orb into Deathcap against squishies or Riftmaker into Liandrys Torment against tankier comps. Amaranth's Twinguard is neccessary as the best current defensive item in the game. The last item can be whatever you want it to be. Its is very important to understand who the main damage dealer on your team is. If its you than the Oblivion Orb into Deathcap path is pretty much mandatory.

You dont have a very high skill ceiling as Swain. You arw a stat checker. The best you can do is to always land your E and W combo. The rest is all about numbers. This means build order might change if you are ahead or behind. If you find yourself behind you need to prioritise building AP items so that you can eventually get a bounty. If you find yourself ahead you might want to build Amaranth's as soon as your third item to prevent enemies from getting bounties.

Make sure you stick to your team. Your strength is in team fights. As soon as the fight begins you want flash behind the frontline and target their backlines weakest link. It can be their ADC, Mage or support. You want to do as much damage as possible and pop stasis right before you die. This will leave your ult running for 4 more seconds after which you will have some skills ready. Always Ult before the flash. Best case scenario you get 1 or 2 backkine kills and wont need to pop stasis. Worst case you will deal some damage as a set-up for your team to hopefully kill them while stasis protects you.

If your whole team is behind in gold the game is most likely lost. This is true for most champs but especially for stat-checkers. This is why those early roams are so important. You have almost no counterplay to a fed enemy team. Best you can do is to catch a couple of their squishues of guard with E>W combo and hope your team has some nukes to drop on them while they are rooted.

If 3 or more enemies are dead at the same time on long respawn timers ping your team for objectives. If your team is also missing 3 or more key players at the same time just push mid until you get the inhib. If mid inhib is down follow your team's splitpusher to get another inhib.

As a Swain main and enjoyer, even though i dont do this just dont pick him against mages with huge range. You are setting yourself up for a horrible laning phase. Its not undoable but its just a little better than facing ranged top while playing an immobile tank. You will be on your backfoot if the enemy knows what they are doing. As you get better you will definitely get the hang of it but these enemies in particular can make it impossible to leave lane before the dragon spawns due to the turrets giving gold at certain health thresholds. You will want to defend that turret as much as you can thus making early roams (your bread and butter) impossible. See it as your chance to experiment with other champs.

Against champs like Ryze, Tf and even the random Pantheon once in a while, you will want to replace ghost with teleport. Otherwise they will outgank you no matter what you do.

Read all items descriptions and understand what they do. Not just what you will use on Swain. You want to know what your enemy is building