The Key to Phages guide is positioning so the entire enemy team is inside your AoE when you die since most bad players tend to forget he's still dealing damage while dead. Also, remember you need time to channel R and it'll get interrupted if your passive times out while you do so. The safe solution is to press R immediately when you die and then resuming lay waste afterwards. Though you may be able to do more damage if you lay waste first and defile as late as possible, as people will have less time to walk away.
I've only played Karthus once in ranked, but we won that game and I managed a triple kill after dying.
That's also very important. I made my guide very brief and tongue in cheek, but, if someone is genuinely curious about pursuing the path of Karthus:
Summoners:
-> Flash+Exhaust. I know that Phantoml0rd is an amazing player and he uses revive+teleport, but seriously, unless you're 2K elo and know you can do it, fuck that shit. You're betting everything on one teamfight with that combo, and will likely die a few times in lane due to not having flash+exhaust. Additionally you cannot flash into their team + exhaust the carry when using revive+teleport. IMO it's better to have a stronger lane phase and a stronger initial teamfight than to revive+teleport to try to clean up mid fight.
Runes:
-> Always use Magic Pen marks. Always.
-> Use mana regen seals most of the time (flat is nicer for laning, but scaling could potentially win you a really close teamfight), scaling HP seals versus a bitch like leblanc or if you just need more health, and scaling AP seals if you just don't care
-> Use flat MR glpyhs or scaling AP glyphs, depends on if you expect them to land harass
-> Use flat AP quints most of the time, movespeed quints if you're afraid their skillshot combo will lead to your death, HP or MR quints vs leblanc/veigar and armor quints vs Talon
Masteries:
-> 21/0/9 getting as much AP as possible from offense and mana regen+buff duration in utility
-> If you're afraid their maokai/lee sin + hard CC mid is going to camp you all game, you could do 21/9/0 if you really want
Items:
-> Boots + potions almost always. I can't think of any situation that you wouldn't get this combo. Even if you're facing the dreaded leblanc/talon/whatever, if they have boots and you don't, they'll be able to land more harass on you.
Now this is where Karthus diverges. I prefer the more traditional (I think) form of building him
-> Rush a catalyst. If you're farming well you'll get it pretty early in the game and it will successfully sustain you throughout the laning phase when combined with potions.
NOTE: every time you go back, try to buy the next piece of your build AND buy enough potions to get you up to 2-3 and 1 ward.
-> After the catalyst you have an option - if you're in no particular danger, then turn the catalyst into a Rod of Ages ASAP. If you're trading a lot, taking a lot of damage, then buy a Hextech Revolver, if you need to move faster to dodge skillshots/avoid ganks, then get Sorcerer's Boots
-> Purchase the items you didn't in the last step depending on if you're safe or need more speed/sustain (sorcerer's boots, hextech or rod)
-> Do you have double AP? If yes turn your Hextech into a Will of the Ancients. If no then rush a Deathcap.
NOTE: If you are facing Veigar/Leblanc buy a Negatron cloak somewhere in there. Assuming you don't fuck up and feed them early, it will mitigate enough damage that even if you get combo'd you won't die. If you are facing Talon and he is dunking on you, then get 1 or 2 Doran's Shields (Sell them later obviously)
From here it's player's choice.
-> If you're slowly dying in teamfights, finish the Will regardless of who's on your team.
-> If you are getting instantly burst, if it's physical, get a Zhonya's Hourglass (try to have your AoE on while you're hourglassed), if it's magical burst decide on if Hourglass, Ryjal's, or QSS (Malz/Veigar)
-> If they have a lot of magic resistence, or you just want to hit them harder get Void Staff
-> If you have Double AP and your other AP isn't getting it, get Abyssal Sceptor
ALSO -> When you complete your set or you're level 16-18 (usually the latter comes first), try to always have an Elixer of Brilliance on when you're going to be fighting. I know that some people, even pros, by these earlier in the game, but I'm honestly too dumb to figure out when it's worth it, so I just wait until the end of the game:patriot:
If you're ROLLIN IN THE CASH and have nothing to spend it on, get Elixer of Fortitude and Oracle's
BUT PHAGE Y U NO ARCHANGELS
so I used to rush archangels. then I stopped and gained 400 elo
In all seriousness, Archangels staff is a very strong item, AP wise. Unfortunately that's all it really offers. If you're not going to suicide into them and are only going to poke them from a range with you Q, then Archangel's is fine. If I were facing someone who was massively worse than me in lane and not damaging me at all, I would consider getting an early Tear of the Goddess and eventually turning it into an AA. This rarely ever happens though.
BUT PHAGE Y U NO GA, U LIVE 3 TIMES LOL
Because when you resurrect you have very little life and will instantly die. You'll also deal markedly less damage from wasting an item slot on the GA.
I may add more later, feel free to ask questions.