If you need to ask, you probably can't.
"Alpha hydroxy" is a marketing term that refers to a carboxylic acid which has a hydroxyl group on the carbon adjacent to the acidic carbon.
If you can get your hands on some alpha hydroxy acids, you could dissolve them and make an "alpha-hydroxy" solution. But do you really want to put something you mixed up at home using a compound with the term "acid" in it on your face? There's a REASON the marketing term leaves out the "acid" part.
Some fairly common and relatively innocuous alpha hydroxy acids are citric acid and lactic acid, if you're bound and determined to do this. In fact, lemon juice is ALREADY an alpha hydroxy solution; if you want something you can make at home.