Learn Icelandic: Húsið er hér.

In Icelandic, you say 'the' by attaching a suffix to the end of the noun instead of using a separate word in front of it. The base word is hús (a house), and adding the suffix -ið turns it into húsið (the house).

Why is the ending -ið here, when I have seen words end in -inn or -in?

The definite suffix changes based on the grammatical gender of the noun. Because hús is a neuter word, it takes the neuter ending -ið. Masculine words take -inn and feminine words take -in.

If I wanted to say 'This is a house', would I still use húsið?

No, if you are introducing the object with 'This is', you use the bare noun: Þetta er hús (This is a house). You only use húsið (the house) when you are making a statement about a specific house we already know about.

Does the verb er change if I talk about myself instead of a house?

Actually, no! The verb vera (to be) uses the exact same form er for both 'it is' (like the house here) and 'I am' (ég er). It is also used for 'he is' and 'she is'.