わたしは料理を独学しようとしています。 'Try to do something' can usually be translated into '...しようとします', while 'try doing something' is usually translated into '...してみます'。

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)

To translate your sentence literally, you can say "自分に料理を教えることを試しています。” Or you could simply say "I would like to learn how to cook" = 料理を習いたいです。 Note: While I am of part Japanese descent, my native language is English, not Japanese, so I welcome all native Japanese speakers to chime in! Your responses will be greatly helpful to me, too. Thanks!