Key strategic elements to consider when playing Abaddon

Apply Aphotic Shield pre-emptively on yourself as you are coming to lane after rune fight. Apply another as the previous one explodes to inflict great AoE damage. Pull afterwards.
Play ahead of the Core you are supporting to absorb damage and trade regen.
Salve or clarity won`t be canceled while you have Apothic Shield on.
If someone applies a break effect on you, you will have to trigger Borrowed Time manually.
If you got disabled along with your teammate you can pop Borrowed Time to remove stun off yourself and then apply Aphotic Shield on a stunned ally to free him as well.
Constantly look at your teammates to heal or hard dispel them.
Silences and heal reductions are a big problems for Abaddon. Avoid being hit by those or itemize against them.
With Aghanim`s Scepter, you will need to activate your Ultimate manually, while most of the damage is being inflicted on your teammates.