You can use ガーデニングする (do gardening) for gardening.
ガーデニング is a generally used term in today's Japan.
So you can say...
- 趣味の一つとして、ガーデニングを始めた。 (As one of my hobby, I started gardening.)
- ガーデニング用品を買う。 (Buy tools for gardening.)
- 子供と一緒にガーデニングした。(I gardened with my children.)
If you don't prefer this word, you can use [園芸]{えんげい}する (do gardening) alternatively.
ガーデニング sounds more modernized compared with 園芸. If you do something in traditional Japanese-styled garden, you cannot use ガーデニング.
[造園]{ぞうえん} or [築庭]{ちくてい} sounds like creating large-scale garden from scratch.
[庭師]{にわし}する(Do gardener) is not a correct Japanese verb.