Swain is a Jack of Trades as Support. He dont excels at anything specific but he is able to take on many roles. You can play him as Tank, Bruiser, Utility Mage or Pure Dmg Mage.

Pros:

+ Versatile
+ Decent Scaling
+ Always useful
+ Carry Potential
+ Extremely fun to play feeling like the Endboss

Cons:

- Squishy early
- Low Range compared to other enchanter or mages
- Cc is tricky to hit
- For higher elos, Kiting/Zoning is required

His passive Stacks life infinitly. Every time you hit someone with or you are able to pull someone with or someone dies and you collect the Soul, you earn 1 passive stack that grants you 12 permanent life and heals you for 4%/5,5%/9% of your max HP. Can Sustain you through lane and extended fights.

Unleashes Bolts that deal dmg per Bolt. Try to be as close as possible to deal more Dmg.

Your Vision Spell for checking Bushes or cancel Backports. Try to use it on every CC to gain easy stacks. Also some Champions have ability animations that are easy to spot and make them unable to move like Cait Q. Try to use W on them while they are immobile for Poke and stacks. Also good to cut off escape routes or to zone adc when he try last hitting minions.

Try to hit it on maxrange so it instantly stuns and dont need to travel back. Also a good tool to zone enemys or cut of routes. Works on more then 1 enemy. If you flash after casting it (or simply move) you can redirekt the claw going back at you.

Your main Sustain. Try to have as many people/minions in your Aoe to drain life. Spare the second charge to slow enemys rather then using it for extra dmg. Also, remember that your Ult works during zhonyas and heals you during the stasis.

Now we cover up in which teamcomps Swain fit. Roughly speaking always look that you are not the only Frontliner. Swain may be Tanky and can sustain himself but you shine in comps where you can engage as second or third person since you can only unleash your dmg and cc if you dont get focused and die too early. If you have a dedicated Tank or Bruiser Champions in Champ Select? Feel free to Pick Swain. Also if you pick him in lower Elo he excel as carry Support.
Champions like: Sejuani, Ornn, Maokai, Lee Sin, Galio, Trundle or Jarvan IV are good examples for that.
Example Teamcomp that is good for Swain:

K'Sante
Lee Sin
Ryze
Jhin
Swain

New Season new Start right? Well, sadly Swain Support is terrible right now. You can still pick him into engage champs like Maokai, Nautilus etc (look Threat Tablet) but hes is overall terrible against enchanter and mage supports. The items are too expensive for him so he gets item spikes way later then other Supporter. Neitherless, in Elo below Gold you should always be able to pick him, but the higher you go the worse he gets rn. On midlane, adc or even Toplane he is insane good tho. So maybe try him there till he gets in a better support state.

Good luck with your newe Season Guys, happy Climbing!