Anti-Mage

You can rush vanguard on tough lanes. Otherwise try to get away with cornucopia.

Hit opponents and burn their mana whenever you can, for example when they go for a last hit.

Play safe and acquire Battle Fury as early as possible. Your farming speed goes up exponentially with it.

Look around the map while you are farming to dodge the ganks but also to potentially snipe a kill with Mana Void.

Plant wards for yourself in the area you are farming.

Keep a lane pushed out to apply some pressure on the map. If you expect to be ganked, Blink into trees and teleport to the opposite side of the map.

With Manta Style you can play more actively and join most of the fights. Prioritize killing backliners and supports.

Wehenever your teammates die consider cutting a wave behind the opponents or push out some other lane.

Anti-Mage is a weak laner, so look to pressure him from the start

Look to spend your mana before it gets burned by Anti-Mage

Against Anti-Mage during the laning phase buy a Magic Stick or consider buying a Soul Ring to have mana for spells

Look to disrupt Anti-Mage's jungling by placing deep wards and smoking on him. Anti-Mage is weak until he gets Manta Style

Consider getting Boots of Travel on one of the cores to address Anti-Mange's split push playstyle

In team fights look to save the hero that Anti-Mage jumps on. But be careful as you might blow up too if you get too close to a Mana Voided hero

Anti-Mage is strong mid- to late-game as he can farm rapidly, but he is not that strong in very late game