I'm EskimoLizard. I am a Diamond 4 Swain player that has a 62% winrate on Swain ADC with 94 games played. I've found through my ranked experience that Swain is one of the best bot laners in the game, and it is extremely easy to win lane with him. I'll give you some of the tips I used to climb with Swain this season.

Laning Phase with Swain is all about throwing out e's off cooldown. You need to stack your passive as Swain in order to be useful, and every time you hit an e, you also get a nice chunk of healing.

Swain struggles to keep up in cs in a lot of matchups, but that's why it's so important to stack your passive. You get a ton of gold value from all of your bonus health that makes up for the gold you may be lacking in cs.

You want to look for short trades as Swain during the early levels. You have fairly long cooldowns, and the enemy adc will have more consistent damage than you early with their auto attacks, so it's best to just do short trades with your spells rather than all in with autos early.

Swain has a massive power spike when he reaches level 6. You will have too much sustain early for most enemy bot lanes to kill you, and since you can keep your ult going forever, you will always have the damage to kill your enemy laner. Basically, as soon as you hit an e, you want to look to all in.

Rylai's is one of the best items for Swain, and that is why I recommend you build it second every single game. Rylai's gives you an insane amount of impact in team fights. You create a massive AOE slow with your ult that makes it impossible for the enemy to escape you. Rylai's also makes it much easier to land your e, so it effectively increases the amount of healing you will get because it guarantees that you will land more e's.