So Swain just got reworked, and probably people don't know most effective and "correct" way to play him, I too don't know and that is why you must understand that is just a idea of playstyle, probably not the best one.

Pros + have a lot of sustain + have an extremly long range on his W Vision of Empire + various forms of CC + is followed by crows everywhere on map (look on walls)

Cons - sometime you will fell his damage is not to good (thats why we use Electrocute to boost his combo damage) - even if is tanky is vulnerable in a lot of situation - W have a long cd - you can stun a minion insead of your enemy if you aren't careful - you can't reactive your ultimate Demonic Ascension until you steal a certain amount of health

Now i must explain probably why these items and for what are good for Swain, well Doran's Ring is a standard item for most ap midlaners, and Dark Seal is a good choice even if you want some sustain or to snowball the game and upgrade it later in Mejai's Soulstealer.
Rod of Ages is the item you must rush first, that because the item is staking in time, so you need to have it as earlier as possible, an alternative for this item would be Everfrost wich have similar stats and an active. These items are great for Swain cause give him all he need: AP, mana and health.
Lich Bane is just a preference for me, probably not as great if we compare with other items, will give some mana sustain, cdr and extra damage from basics after you use a skill, and that is great cause basic damage from Swain is extremly low to can count in a fight. I would consider and Nashor's Tooth in his build, but Swain is not an aa champ to try focus on it.
Liandry's Torment is great cause offer some health and magic penetration, perfect for Swain kit.
Zhonya's Hourglass Can save you from a lot of situation and have a nice interaction with your ultimate
Spirit Visage is a great tanky item, not offer you ap, but insead offer a lot of health, magic resist and increse the amount of healing you recive from any source, what work great with your passive and ult. (btw i associate Swain with Vladimir in some cases and that is one of reasons i choosen Spirit Visage (i built it and on old Swain as well, but the new Swain is completly changed in style of play)

Right now I'm to tired to talk about every rune in part, so i will mention just the important things.

Principal runes would be Sorcery with any keystone, from what i seen all can work .. more or less or Domination with they key stones Electrocute
and Secondary runes in order of importance:

• Inspiration for Perfect Timing #leagueofstopwatch
• Resolve for Revitalize wich will increse your healings.
• Sorcery for The Ultimate Hat and/or Gathering Storm
• Precision for Triumph or Presence of Mind

So how i said in start of guide Swain just got reworked, and that mean you can't just create a perfect build from him from start just as simple, best way to build him is to associate him with other champions style and start from there, from example i alerd said my inspiration for Swain build started from Vladimir, cause they have a lot of things in common (a lot of sustain, can be played tanky, low cdr, slows), also you can compare him with Fiddlesticks or Karthus, that type of champion who can jump in middle of enemy team and damage they without problems waiting to be focused and then using Zhonya (what will not interrupt his ult). Also can be played safe staying in back lines and attack with your skills (E and W).

In lane best way to abuse Swain directly from start is to start with Nevermove, his range is enoguh to safe poke your enemy and proc Ravenous Flock wich will drag him close to you and deal bonus damage.
To abuse Swain maximum in a duel use Nevermove to stun the enemy, then drag him with your passive and hit with all bolts from Death's Hand, use Vision of Empire even to catch him or to execute him if somehow escape from your combo. Remember, Vision of Empire have a delay of 2 seconds. Play Video