"I do not cook very often."
りょうり as a noun means 'cooking' or 'cuisine'. As a verb (りょうりをする） it means 'to cook'. あまり means 'not much'. しません is the negative form of する (to do), meaning 'do not'. あまりしません combines to mean 'do not do much'.
Put it all together and you get: 'Cooking (I) do not do much', or '(I) don't do much cooking'.
If that doesn't clear it up for you please try to be specific about what you're having a hard time with.
Ryouri りょうり is cooking (as a noun).
To make it a verb you attach します (dictionary form する, "to do")
りょうりします "I cook"
りょうりしません "I don't cook"
Amari あまり is used to turn a negative verb from 100% negative to "not really" or "not much":
しません "I don't do it"
あまりしません "I don't really do it"
In this case the topic particle は has been used to make りょうり the topic. It's broken down like this:
りょうりは、 "About cooking..."
あまりしません。 "I don't really do it."
I THINK you could also say あまりりょうりしません if you didn't want to make りょうり the topic.