Truthfully, there is not much of a difference. 1. "I like to do (something)" is, for example, like saying "I like to run." 2. "I like doing (something)" is, for example, like saying "I like running." "I like to run"= "I like running" "I like to do dishes"= "I like doing dishes" The main difference is how commonly each phrase is used. There are some instances where using the infinitive "to (verb)" would be more common than the progressive "-ing" form, and vice-versa. The only other difference I can think of is that "to do" is a true verb, while "doing" may be either seen as the progressive form or, perhaps, a noun (as in, THE ACT of doing). Remember, we do not put "do" or "doing" in front of all verbs when we discuss activities we like. Only use the word "do" or "doing" if that verb is a part of the activity. (i.e. do dishes, do sit-ups, do housework, etc.) Source: American English (self)

I like doing gardening. Weeding is one of the things I like to do in the garden.