なるべく + [verb] なるべく + [i-adj] なるべく + [na-adj] なるべく + [verb ない-form] + ようにする
なるべく means "as much as possible", "if you can". It is an adverb, and it goes in front of the verb or adjective it modifies.
With ようにする, it describes a habit you try to keep, and with a ない-form, something you try to avoid.
The two swap in most sentences. できるだけ is "as much as you can", pushing towards the limit of what is possible; なるべく is closer to "where you can", and leaves the listener more room, which makes it the gentler choice for a request.