You can also say "Olen kaksikymmentäneljä vuotta vanha."
"Vuotta" is the accusative case of the word "vuosi".
Kids say: "Olen neljä." "I am four." Well, I could say also: "Olen kolmekymmentäseitsemän." :) So, the verb is "be".
You could check out the Finnishpod101.com -site. They have a free trial period. Maybe you find some material. At least the Greek page is nice... You could also google "Finnish as a second language", in Finnish "suomi toisena kotimaisena". The vast majority or Finnish material is found, of course, here in Finland.