Tháinig sé isteach . . . . he came in and asked me to give him a hand of help i.e. a helping hand.

Tháinig sé is past tense of tar - - come

isteach - - in (with movement). Isteach refers to the movement of going in. If you said d'fhan sé istigh - - he remained within or inside istigh refers to where he remained, his location without movement. There are many words like this which have one form for the movement involved and another for the station or location. I will list them later. Isteach and istigh were discussed earlier in this lesson.

d'iarr sé orm - - he asked me (to do something) This is past tense of the verb iarr.
If you wish to enquire or ask for information use fiafraigh - - ask (for information), enquire.
D'fhiafraigh sé díom cá raibh Brian ina chónaí - - He asked me where Brian lived.

Note that iarr is followed by ar and fiafraigh by de. Verbs taking preposition like these have already been presented in these lessons. Click here to see them again.

Lámh chúnta - - a helping hand. "Help me" however would be "cuidigh liom" or "cabhraigh liom"

a thabhairt dó - - to give to him is claoninsint or reported speech for the command "Tabhair . . . dom" - - give me. Once the basic tenses of the verbs have been presented I will deal with claoninsint - - reported or indirect speech.