The mobility of Anti-Mage allows him to choose the way he approaches a team fight and gives the player a variety of viable options.
Which targets to focus?
You have three types of targets you can focus in fights.
First, you can Blink in on a support, use Manta and try to quickly bring it down before he/she has a chance to have an impact in the fight. Even though supports are usually positioned quite defensively Blink gives you the opportunity to reach such targets almost instantly.
Second, if you have Basher of Abyssal Blade you can jump on an enemy carry. Preferably, in that case, you will follow up a disable of your allies on the opponent and with the help of your fast AS and Bashes prevent the enemy carry from efficiently fighting back. You can also jump on a squishy but elusive hero and lock him/her down with Abyssal Blade, disabling your target from running away. You can even try to jump on a BkB-dependent hero and try to stun him before he can use his BkB, giving your allies a valuable window of opportunity to use spells on the target.
Third, you can go on a mana-dependent hero, use your Manta and burn his mana so that he can’t use his spells in fights. Even if you don’t manage to finish the kill you would have created a big problem for the hero – he needs its mana to have an impact in the fight. Even more importantly, by doing this you create a very good target for Mana Void later in the fight. If the target is close to any other opponents you can deal a massive AoE nuke which could win you the fight.
Entering the fight:
What you need to be careful about is how you close the gap between yourself and your enemies. If opponents have a lot of disables and DPS and you are not survivable enough, Blinking in might quickly lead to your death (since you will have your Blink on cooldown and won’t be able to get away). Therefore, in such a case it might be better to walk in the fight and keep your Blink as an escape tool. The other option is to jump on a target which is somewhat far from any other opponents. If the allies of your target want to assist him/her they will have to walk a certain distance – this should give you enough time to retreat (either by running or by waiting for Blink) and avoid getting in danger.
If you are survivable enough, however, it is way better to use the Blink to immediately get to your preferred target in the fight – this will make kiting you much harder and could net you quick kills.
Ideally, you don’t want to be the first hero to jump in – you go for BKB relatively late and if you are the first available target for your opponents you are likely to get disabled. The perfect scenario is that your allies initiate and manage to control the enemy team and then you immediately Blink on the squishiest high-priority target and burst it down before the disables are over. With an Abyssal Blade and BKB, however, you can be a very potent initiator yourself. Blinking and immediately disabling a high-priority target will allow your teammates to follow up and allow you to get the kill.
By using your Blink you can quickly reposition yourself and switch targets during the fight. For example, you can jump in and kill a support then Blink towards the enemy carry hero that got disabled by one of your allies.
Using Mana Void:
Look for enemy heroes that have lost a lot of Mana during the fight and use your ultimate on them. You can use it to burst heroes when they are escaping on low HP or cast it when heroes are grouped up to deal a lot of damage in an AoE.
In the ideal situation you will manage to use your ult on a low-mana target which is close to other opponents, however, this doesn’t happen very often. Because of this, you need to find a balance – don’t save your ultimate for too late, killing an important opponent with it can win you the fight. At the same time if you use it too early you are probably going to have a low impact with it (most heroes are on full mana at the start of the fight) and you might miss a very valuable opportunity that comes later in the fight because your ult is on CD.
Video example: