So, before moving to Dota2, I played a lot of matches with Abaddon - a fucking lot, he was my main for like 1 year-, it was really fun and I picked up some things:
My main build was support, it has to be 3rd/4th in the team, cant be used as 5th hero.
Items to get ASAP:
ManaBoots
Mek
Spells:
Prioritize Death Coil, get Shield as your second spell. Death coild has a huge range, useful to heal allies far away from you, damage enemies that are trying to escape. Often caughts enemies by surpries with its low cd. Use it to heal ally often, try to not be inside the fight but still stay around so you can cast shield too and stay healthy enough to keep casting DC (it cost some HP to do so). You can deny yourself with it, I did it pretty often after letting my teammates scape.
Edit:
Why is it useful to not be in the middle of the battle: You pay 125 hp to heal 250hp, is better for you to pay the hp to heal someone, than to lose 250 hp yourself in battle
/Endedit
Shield is a amazing spell, blocks ups to 250 damage, explodes once it reach the threshold and damages around for 250 damage. Also it dispells all debuff on the ally unit so is really really usefull in battles, use it after a key ally got disabled/silenced/tracked/etc (doesnt work against Doom ultimate, except for 1 rare case in wc3 dota) Example: your clinks just got hit by Dust, shield him so the dust debuff dissapear. Your support just got hit by a long range Mirana arrow, 4-5 sec stun. wait till mirana jumps in to shield him out of the stun, and counter attack. Or use it early to escape.
If you need to use the shield before going into a battle do it at 4-5 secs before the clash. You want to have that shield up again to dispel disables and stuff in the middle of the battle.
He has some mana problems, but getting boots solves it. Boots on allies as well as you can turn your push into real sieges with no need to go back for heal.
Try to heal/shield/mek that one hero being focused, even if its a support, creating a situation when the enemy has to choose to change targets because they are afraid of the shield aoe damage(and lose whatever advantage they got) or keep focusing on him taking longer than it should so your allies can pick of their supports. You really work well in 3+ man push/fights.
Enemies will try to focus you if you save allies or delay their deaths too much, do not worry! Your ultimate will keep you alive, remember this trick: If you use DC when using your ulti, you will get HP back instead of paying it. If you cast DC when you have shield and ultimate active, you will get TWICE the HP back. Actually, if you get hit by whatever spell/attack when you have ult+shield up, you will get twice the HP back.
You can manually cast your ult to get some extra HP when the enemy does not expect it. For example, if you see a enemy pudge used hook and you cant dodge it, activate ult before the hit, you will get +360 hp (iirc) and the enemy pudge will most likely start the dismember before he realises you are recovering hp.
After that, items are situational and depends on how good your team is doing. I generally go for Pipe and make the team push for the win with almost unlimited health.
Edit: one more thing:
You can break your shield by using Death Coild, Pretty fun to do it when chasing. go after a low hp hero with shield and DC him to death, the DC will kill him, IF NOT, the AOE damage from the shield (activated by the sacrificed HP for DC) will kill him