A phrase like "ich möchte gern..." is typically used to request something or to ask for permission to do something. The translation you quoted, "I would like..." is quite accurate. In combination with a verb, it would be something like "I would like to (do something)".
Ich möchte gerne Fieber messen im Ohr.
would be something ...
The German word »gern« usually means "to like". Your sentences are good examples for that.
Susi isst gerne Brot.
Susi likes to eat bread.
This means, that Susi often eats bread because it tastes good to her. The usage of "to enjoy" seems too strong for this sentence, because means to relish something, to have doing so, but for Susi ...