Swain is a good champ to main. Usually when you start off you have a low winrate and as you get more experience with this champ the winrate rises considerably. He can also be very rewarding to play as he is one of the hardest snowballing champions in the game. Fed swain = gg rito.

Pay attention to the champion you are going to play against. There are some champions which you are supposed to win from in the early game, others you are supposed to farm against and just outscale.
Pick runes according to their damage but always take flat ap quints and magic pen marks for enough trading damage.
Masteries are as shown in this guide.
summoner spells. Swain does not have a gap closer or maker so flash is essential. Ignite is for adding that extra bit of damage and preventing your opponents from healing through you slow (but high!) damage.

The plant with swain is to harass you opponent down efficiently before level 6 and maybe even get some kills. Dont take too much risk however because level 6 is when you can start taking trades which are unfavoured at first and then heal it back up again.
In the late game you want to be a center piece of attention while your team can dish out damage. Swain usually isn't a splitpusher but he can do that aswell. The most important tips and tricks are shown in the ext chapters.

Take note of which enmy champions are able to kill you with their full combo and stay away from them when you do not have zhonyas. It is imperitive to keep tracks of your flash and zhonyas to ensure you will not die to assassins.

Trading with swain is very dependent on your ability to farm with autoattacks. You want to use your autoattacks and you auto attacks only on swain to farm. It doesnt matter if you don't get all farm but try to get as many as possible. once you get accustomed to his animation farming can be quite forgiving. Only under tower will you ever use abilities to get some farm if you woud otherwise miss too much.

The rule is however you can kill most champions in lane by harassing them and when they are down to about 40% hp all in them with W + E + Q Ignite Combo quite easily.
Here is what the early game should look like:
https://www.youtube.com/watch?v=3zbHHtEUFH0
In this video you can see that farm is taken with autoattacks and swain doesn't lose any mana even though he trades with his e + AA as mucha s possible. The autoattack does a considerable amount of damage so don't forget to add one! At level 2 he Q adds some nice extra damage. In this video he takes W at level 3 only because he knows he will need it for all in. Usually you will need to poke some more still and so an extra point in e is more value. W is not for trading! only for all in!
Try to add 3 sources of damage to every trade. This will proc thunderlords decree (cooldown can be seen in the lower right part of your screen). And that adds a large amount of damage to your combo. This is usually not possible yet at level because you dont have q yet.

At level 6 you can use your ult to all in aswell. Ult is not used for poking jut as w! it can be used to push and heal up effectively but not when you dont have enough mana.

In teamfight you are usually not able to poke because the enemy team has a longer range than you. Dont be afraid to use an E for someone who overextends however.

Your main focus is chosing the right time to engage. When is this time toe engage? When the enemy has used some of their abilities which they would have needed to kill you with. So for a syndra this her stun, or for lux her snare or for an amumu his q. These ablities have a fairly long cooldown and when some of them are down that is the time to engage.

Engage can involve flashing but usually you will want to use it to flash over certain abilities. Then rylais (which you will hopefully ahve at this point) will help you stick to your targets. Swain wants to kill squishies just as much as any other champion. However standing at up to 3 (more enemies can't be targeted by your ult at the same time!) can be a huge boost to your healing. Just try to dodge cc.
Zhonyas is used in teamfight under 2 conditions: 1. you are standing nearby enemies and 2. You are either ignited or under 40% hp and about to receive some high amount of damage.

When you pick swain the chance is high the enemy team will pick ignite. This is not a solution to a fed or even swain however because the ignite will wear off during zhonyas.
Also watch out for morellonomicon, this item will half your healing when under 40% hp. In this case you will want to zhonyas above 40% health!