The Japanese counting with つ (~tsu) endings are used for counting "OBJECTS" (non-living objects).
The complete list for counting objects from 1-10 are:
1=ひとつ(hitotsu)
2=ふたつ(futatsu)
3=みっつ(mittsu)
4=よっつ(yottsu)
5=いつつ(itsutsu)
6=むっつ(muttsu)
7=ななつ(nanatsu)
8=やっつ(yattsu)
9=ここのつ(kokonotsu)
10=じゅっこ(jyukko)
And as Daniel said, in Japanese you have to use different counter words for different categories. For example, for people, for animals, for long objects, for flat objects, for stories of an apartment etc.
Here is a short video that will give you more ideas about Japanese counters.
http://www.youtube.com/watch?v=DDRbzW8AWEI
If you want to learn all the counters, then you can learn it from here:
http://www.tofugu.com/guides/japanese-counters-guide/
Please remember, at first these counters seem to be very confusing and hard to remember/understand/memorize, but with regular use you will be able to master them in no time and will actually seem fun! Try counting things around you using Japanese counter words and gradually you will get the hang of it (^_^)
I hope my explanation was helpful ;)