Saturday — the pottery class I started going to last year.

Literal

Saturday, last-year from go-started pottery class.

Sentence-fragment diary/blog-style construction ending on a bare noun. The verbal phrase 去年から通い始めた ('(I) started going from last year') is a relative clause directly modifying 陶芸教室, with no explicit relative pronoun and the subject (the speaker) silently omitted. ~始める is the auxiliary 'to begin to.'