Counting in Japanese is much harder than counting in English. First of all there are 2 counting system. Most of you have probably heard

1. ichi
2. ni
3. san
4. shi
5. go
6. roku
7. shichi
8. hachi
9. kyuu
10. juu

etc... but there is another,

1. hito(tsu)
2. futa(tsu)
3. mi(tsu)
4. yo(ttsu)
5. itsu(tsu)
6. mui(tsu)
7. nana(tsu)
8. yo(tsu)
9. kokono(tsu)
10. tou

The second counting method is a prefix which is why I put the tsu in parenthesis. It also only goes to 10. After that you switch back to the 1st but it is used quite often. Then to make it more compliated there are exceptions

First of all, in the first counting system, 4 can be yon or shi and 7 can be nana or shichi. I depends on what you are using them for.

So for example July or the 7th month is Shichi−gatsu. But 7 yen is nana en.

Another exception is in counting people, 1 person is hitori, 2 people are futari using the second counting system. After that though it's back to the first. 3 people are san−nin, 4 people are yon−nin.

There are more special exceptions too. Days are counted using the second system except for day 1. ichi−nichi, futsuka, mikka, yokka,

But, if it's days of the month then the 1st day is tsutachi and the 14th, 20th and 24th are also exceptions. The 12th is juu−ni nichi (12th day), the 13th is juu−san nichi (13th day) the 14th is juu−yokka. The 20th instead of being ni−juu nichi is hatsuka. 20 years old is hatachi, another exception, not ni−juu sai (20 years old)

But, it gets even worse. When counting in Japanese there are counters. An English example would be cattle. Although it's perfectly reasonable to say "there are 12 cattle" it's not uncommon to say "there are 12 head of cattle". In this case "head" is the counter for cattle. Well, in Japanese EVERYTHING uses counters and there are literally hundreds.

Paper and other thin objects use mai. ichi−mai, ni−mai. Small objects use ko, ni−ko, san−ko. Small animals are hiki, yon−hiki, go−hiki. Birds and rabbits are wa. ichi−wa, ni−wa. Big animals use tou. ni−tou, san−tou. Cars are dai. ni−dai, san−dai. Books are satsu. ni−satsu, san−satsu. Here's a list of a bunch of them.

On top of that, depending on the counter there are more exceptions. For example even though the counter for small animals is hiki they get counted like this

1. ip-piki
2. ni-hiki
3. san-biki
4. yon-hiki
5. go-hiki
6. rok-piki
7. nana-hiki
8. hap-piki
9. kyuu-hiki
10. jup-piki

To English eyes that looks more strange than it does to Japanese eyes because in Japanese, hi,bi,pi are all the same letter, just with different accents. Think about it, as you say hee, bee, pee your mouth is pretty much doing the same actions so you can see that it's reasonable to think of them as basically the same thing.

Of course to the foreigner learning Japanese this system is hard to get used to and it's mostly through memorization and usage that you eventually learn some of it. But, take heart, even the Japanese have trouble with it. So much trouble that there is a comedy skit / game show where people count in chant. Each person has to count the last thing the previous person said. So for example the first person will chant, "start ban−ban person ban−ban" (ban−ban is just part of the chant). The next person in rythym has to say "2 people" since the last person said "person" last so he might say something like "futari ban−ban rabbit ban−ban". He's free to chose any word to pass to the next person. Person 3 might says "ni−wa ban−ban book ban−ban" and so on. The first person to mess up get's punished. 😃

Update: Okay, a little advice. If you are just visiting Japan and are learning for the sole purpose of buying stuff you should learn the second style of counting. Hitotsu, Futatsu, Mitsu etc because for quantities under 10 that's the most common way to buy something in a store. You can just point and say "futatsu kudasai" (2 please). Of course you can just point and then hold up 2 fingers and say nothing.