Hi!
In German, you have basically 3 kinds of prefixes for verbs :
-separable (trennbare Präfixe) ;
- inseparable (untrennbare Präfixe) ;
- those that can be both (choice to be made according to their meaning).
You can see a list of prefixes here :
http://www.nthuleen.com/teach/grammar/sepinsepprefixexpl.html
In your example, the verb is ANFANGEN.
"An" is a separable prefixe, which means that throughout the conjugation, it will be written in two parts.
- er fängt heute um 8.00 Uhr an (present)
- sie fingen an zu singen (they started to sing)
Exceptions :
- infinitive --> wir möchten früher anfangen (we'd like to begin earlier)
- nouns made from infinitive (das Anfangen)
- past participle, written in one word, but -GE- will come in between --> er hat angefangen (he has started)
The place of the separable prefixe may vary a bit depending on emphasis, but that's not important for now :)
Have a nice day!