、、。
For most subjects, if you don't firmly master the basics at the start, you can't pick them up smoothly going forward.
Literal
Most [genitive-の] subjects [topic-は], first [in-に] basics [object-を] firmly not-do-[if-ないと], that-beyond smoothly acquire thing [subject-が] cannot-do.
A study-advice sentence. 大抵 ('most,' 'generally,' 'for the most part') is an adverb/quantifier used both predicatively and attributively. 学芸 ('academic subjects, arts and sciences') is a slightly formal compound for fields of study. しっかりやっておく combines しっかり ('firmly, thoroughly') with やる + ~ておく ('do and leave in place'), meaning 'do it firmly and solidly as a foundation.' ~ないと is the casual 'must' construction (short for ~ないといけない), here embedded in the larger sentence as a conditional. その先 ('beyond that,' 'from there on,' 'the future beyond') is a temporal/spatial term for subsequent development. The whole sentence is classic educational-advice prose.