How Do I Figure Out My Dogs Breeds?

Most of the time it is based off of physical traits or by knowing what the parents breeds were. Other than that, the only suggestion for specific breed information would be getting a DNA/genome test done. I think that's a little much seeing as you are not trying to prove a pedigree to breed your dog.

I would check online. Look up dog breeds, and find a list. Then, check the colors and personalities that aren't like bichons. It's not too accurate, but it's what I would do.

I would use a resource to look at different breed features and then try to decipher.  
There's a bunch of pictures of the different main breeds on the Internet, such as here at this website:
www.breedersdirect.com