"I want eggs."
Translation:मुझे अंडे चाहिए।
चाहिए is always used with the dative form of a pronoun (मुझे, तुम्हे. उसे etc) or a noun+को.
You can also translate 'I want eggs' as 'मैं अंडे चाहता हूँ। ' which preserves the structure of the English sentence.
In this case, both sentences mean the same and the second one is perhaps not used so often. However, in general, चाहिए implies a stronger/more immediate desire than using the other forms of चाहना.
Eg: मैं पैसे चाहता हूँ। - I want money मुझे पैसे चाहिए - I want money (now) / I need money