"gerne" translates directly to "gladly" and is always used as an adverb, not a verb (as in "like to").
"Ich würde gerne" means "I would gladly" and in context could imply "like to" but doesn't have that direct meaning. For example "Ich würde gerne ins Kino gehen" translates to "I would gladly go to the cinema". In English we wouldn't say it this way and would likely say "I would like to go to the cinema"; however, in German the word "gerne" is often used instead of directly saying "Ich möchte" (I would like to) or "Ich will" (I want) as "I want" is considered too direct and could even be taken rudely (for example when ordering at a restaurant).
Hope this helps!