To continue on, make a living, or get by (often implying managing despite difficulties).
新しい仕事を見つけて、これからもなんとかやっていくつもりだ。
I've found a new job and plan to manage from now on.
少ない給料でも家族で協力してやっていくしかない。
Even with a small salary, the family has no choice but to cooperate and get by.
慣れない土地でも友達がいれば、どうにかやっていける。
Even in an unfamiliar place, if you have friends you can somehow get by.
将来のことは心配だけど、一日一日を大事にやっていこう。
I'm worried about the future, but I'll take it day by day and keep going.