The most simple and natural way in your case would be 料理を練習しています。
I'm not disagreeing with Tangoya-san, but 独学 may be more appropriate for learning some knowledge/skill yourself that many people go to school to learn, such as language, math, computer programming, etc.
In other cases, ....ようにしています or ようとしていますwill do.
For example,
'I'm trying to sleep 8 hours a day' 1にち 8じかん ねるようにしています。(trying to keep a good habit)
'I'm trying to sleep now, but it's difficult because I had 10 cups of coffee today' ねようとしています。でも、きょう コーヒーを10ぱい飲んだからむずかしいです。
(tying to do something at the moment)