1. Laning phase
During laning phase you are looking for an opportunity to engage with w q and hit both enemy laners preferably. Then you chain your E and chase with phase rush if you have kill potential or run away with it if you were just looking for a short trade. Try to get T5 boots druing lane and go roam if the enemy bot is base or you just went back.

2. Mid game
Now it's your time to shine with your runes. You should be constantly roaming around, warding, ganking and clearing vison. Help out the other lanes and get objectives.

3. Late game
In the late game you should keep the objectives warded and look for opportunities to engage fights.

W Q combo
Most important is your W Q combo. You simply W an enemy and spam Q once you start charging. Then chase the enemy down with phase rush and E. This is your bread and butter combo. Use it in lane and in teamfights to cc the enemy team. Try to make engages in choke points to assure you hit multiple enemies with your Q.

Q F combo
This combo is also quite important on Alistar. Start it by pressing Q and then instantly flashing on an enemy you want to knock up. The knock up will appear at the new location. This combo is a lot faster than Flash Q and leaves the enemy no time to react. If flash is on cd you can use Hex flash to make F Q engages over walls and out of bushes.

Your ultimate
You should usually use your R after you engaged and the enemy team is turning on you. It also breakes CC so it might be worth to wait for an important cc like a Morgana binding to ult. You can also use your ult to run away after being caught. Keep in mind that if play phase rush Alistar you are a lot more squishy than an Aftershock Alistar so don`t stick around too long in the fights and re-enagage when your Q and W are back up again.

W Q F
This combo is a great suprise tool, you W Q a minion or other champion while the carry for example stands further away. Then u flash instantly on him like with the Q F combo. Noone will expect that combo and it can decide teamfights.