I would like to know how it would work if I opened a desinging site and charged for euros which i would then convert into usa dollars when i receive my check in the states.
Use http://www.xe.com/ to get the rates. Just let people know what the rate is, and they pay you according to it.
If you do it that way and you make lets say 200euros per cheque that will come out to around $400 it is pretty much double. I don't know if American and Canadian clients will be happy with having to find conversion rates though.
Why charge in euros? USD is the main currency used (I live in the UK and often have to work in USD instead of GBP). Your best to provide a currency converter type thing on your site to set the prices (so the user chooses where they are from and your site sets the currency accordingly).