When to use inde or ind?
Ind shows a direction that a motion is happening (Han gik ind i huset = He walked inside the house (from the outside))
Inde shows position (Han gik inde i huset = He walked (around inside) the house)
There are other adverbs that do the same, that work with prepositions. Some examples are (the positional forms added in the brackets): hen(ne), ind(e), ned(e), op(pe), ud(e), hjem(me), over(/ovre)
Edit: Just a side note, you can add her or der to the beginnings of any of these, when not used with a preposition. For example:
Han står derovre = He's standing over there
Jeg er herhjemme = I'm at home
Jeg kastede det derop = I threw it up there