Alistar can and probably will engage as soon as you get into range. Try to stay at max range at all times to limit his ability to engage with his WQ.
Even though Alistar’s Headbutt W is a point and click ability, you can still dodge it by dashing, blinking or Flashing before it hits you. You can also interrupt the dash with knock-ups, knockbacks or knockdowns.
Alistar will look to roam if the lane gets stale. Make sure to punish him by looking to fight the enemy ADC or zone them away from farm while he’s gone. Make sure you ping as soon as he leaves lane so your allies know he’s gone.
Alistar will not hesitate to Flash over walls to start fight. Be sure to ward your flanks when sieging an objective or starting the Baron or Dragon.
Alistar’s Ultimate R provides him with a ton of extra defensive stats. In team fights, don’t focus him as it will be very hard for you to kill him. Instead, try to peel back and wait for his Ultimate R to end before focusing him down.
Avoid grouping very closely as a team and never stand together inside the jungle. Alistar’s basic WQ combo has a rather large AOE and you may lose the team fight if he can get a multiperson knock up.
At level 1, make sure to harass and poke Alistar with basic attacks to get his health low before he reaches level 2. His level 2 all-in is pretty strong, so you should try and get a health advantage to make it impossible for him to engage.
Once level 6, Alistar can engage freely and tower dive with his Ultimate R. If you’re lower than 50% health, make sure you recall as he can easily tower dive and survive thanks to his R.
Once Alistar picks up Mobi Boots, he can roam and help other lanes. As soon as he leaves lane, ping that he is missing. Communication is key and you need to communicate with your teammates when he’s gone.