Learn French: Elle est sûrement à la maison.

It is built from the adjective meaning "sure" or "certain". To make it an adverb, you first take the feminine form of the adjective, which is sûre. Then, you simply add the ending -ment to get sûrement (surely).

Why does the "u" in sûrement have a circumflex accent (the little hat)?

It inherits the accent from the adjective sûr (sure). That accent is very important because it tells the word apart from sur, which is a preposition meaning "on". When we add -ment to make the adverb, we keep the accent.

Could I put sûrement before the verb, like "Elle sûrement est..."?

No, French is quite strict about where adverbs go! Unlike in English, you cannot put an adverb between the subject and the verb. Short adverbs like sûrement must be placed immediately after the conjugated verb, making it Elle est sûrement.

Why is there a la in à la maison if the English translation is just "at home"?

In English, we drop the article for "at home", but French requires the definite article la because maison is a feminine noun. You must always say à la maison (literally "at the house") when you mean "at home".