Learn Icelandic: Ég þarf að hjálpa þér.

The verb hjálpa (to help) always forces the person being helped into the dative case. Þér is the dative form of þú (you). Many Icelandic verbs require a specific case for their object, and hjálpa is a very common one that takes the dative!

If I want to say "I need to help him" or "her", do those pronouns also need to be in the dative case?

Yes, exactly! Because the verb hjálpa dictates the case, anyone you help must be in the dative case. For example, "I need to help him" is Ég þarf að hjálpa honum, and "I need to help her" is Ég þarf að hjálpa henni.

What is the purpose of að in this sentence?

Here, að works just like the English word "to". It connects the active verb þarf (need) with the infinitive (dictionary form) verb hjálpa (help), giving us "need to help".

Is þarf an irregular verb? I expected the "I" form to end in an "a" or "i".

Yes, it comes from the verb þurfa (to need), which belongs to a special group of slightly irregular verbs. In the present tense, the "I" and "he/she/it" forms don't take a standard vowel ending, so "I need" is simply ég þarf.