Generations
The first generation (F1) standard size Goldendoodle was the first to be bred. It is the product of a Standard Poodle crossed with a Golden Retriever. Most first generation vary with shedding (some more than others).

The backcross (F1B) Goldendoodle is produced by crossing a F1 Goldendoodle with a Poodle. F1B Goldendoodles will have a higher success rate for non-shedding, and are recommended for families with moderate to severe allergies.

The second generation Goldendoodle (F2 or F2B) is produced by crossing the F1 Goldendoodle with a F1B Goldendoodle.  They also have a higher success rate for non-shedding and are recommended for families with moderate to severe allergies.

The third generation Goldendoodle (F3) or often times referred to as Multigen is produced by crossing the F1B or F2 with another F1B or F2 Goldendoodle.  They're like the F1B's and will have a higher success rate for non-shedding, and are recommended for families with moderate to severe allergies.

F1 = Golden Retriever x Poodle
F1B = F1 Goldendoodle x Poodle

Goldendoodle to Goldendoodle
Simplified to say "Multigen"
F2 = F1 x F1 
F2B = F1 x F1B 
F3 (Multigen) = F1B x F1B; F1B x F2B; 
F2 x F2; F2B x F2B; ETC

Temperament
Goldendoodles are very intelligent and an obedient family companion. They are everybody's friend and devoted to their family. They are friendly towards children, other dogs and pets, and easy with strangers. They are social dogs, happiest when with people. Goldendoodles are likely to get into mischief and develop behavior problems if they spend most of their lives alone. Their intelligence, eagerness to please, and love of learning make them very easy to train.
The Goldendoodles ancestry along both parent lines is as hunters and water dogs. The physical appearance of the Goldendoodle runs anywhere from a shaggy-looking retriever to a relaxed-curl poodle, but usually it falls somewhere in between. The length when left unclipped grows to about 4-8 inches. The color of the coat can be cream, red, white, gold, apricot, chocolate, black, parti or merle. This color variation is because of the genetics in the Poodle and the Golden Retriever. 

Poodles, whether Miniature, Moyen or Standard are used for the Goldendoodle breed. Unlike some Labradoodles there is no other mix of breed in a Goldendoodle except for the Golden Retriever and Poodle.  Goldendoodles can range any where from Petite to Giant!    
Finnegan - F1 Miniature
Golden Retriever X Miniature Poodle
Most F1 Goldendoodles are light to moderate-shedding, and most live easily with families with MILD allergies. Families with moderate to severe allergies often find that Goldendoodle backcrosses (F1B), second Generation (F2B) Goldendoodles or (F3) are better because the shedding is not as prevalent.
The gentle-nature of a Goldendoodle.  This is Tess -- Tess is going to be approximately 50 pounds (father Montegue and Chloe -- see more of this previous litter).  Tess lives in Woodstock with my brother.
Some Things to Know About Goldendoodles