、、。。
Come on, Ken'ichi, climb along that gutter. I'll pull you up.
Literal
Look, Ken'ichi, there [gen-の] rain-gutter along-[come-ておいで] [emph-よ]. Pull-[give-てあげる] [because-から].
伝う 'to go along (a guiding surface)' is the verb for moving alongside a wall, gutter, river, or similar line — here in its conjunctive form 伝って feeding into おいで. おいで is a gentle imperative derived from an honorific verb, very common when speaking to children or intimates. ~てあげる 'I'll do X for you (as a favor)' marks the speaker as a benefactor; the trailing から 'because' leaves the apodosis implicit — 'because I will pull you, so...'.