Learn Swedish: Barnet kan inte sova. - The child cannot sleep.

Kan (can) is a modal verb. Just like in English, modal verbs in Swedish are followed by the dictionary form (the infinitive) of the main verb. The infinitive form of sleep is sova.

Do I ever need to put att (to) before sova?

Not after modal verbs like kan, vill (want to), or måste (must). Swedish goes straight from the modal verb to the bare infinitive sova without using att, just like we say can sleep in English instead of can to sleep.

Why does inte (not) go between kan and sova?

In a normal Swedish sentence, the word inte always goes right after the first verb (the conjugated verb). Here, that is kan. The second verb, sova, has to wait until after the negation.

I remember the word for child is barn. Why is it barnet here?

Barn is an ett-word. To say the child, Swedish attaches the definite article to the end of the noun. So, ett barn (a child) becomes barnet (the child).