A genogram is like a family tree, a diagram showing your family relationships, but it's more detailed and includes symbols to show things like, how family members relate to each other etc. Social workers use them to evaluate emotional/social relationships within a family. Other genograms are health ones with symbols for depression, cancer, Alzheimers and so on which health professionals use. So it will look like a cluttered family tree with more lines and symbols than normal.
Because they can be complicated, I'd focus on only your close relatives (like parents, grandparents, siblings, neices/nephews, cousins, aunts/uncles and that's about it) and then any further out relatives who will be involved with your adopted child and you will be seeing
So your genogram would have specific lines and symbols for - seperation, divorce, birth children, adopted children, miscarriages and abortions. But also, in relationship/emotional terms, line representing - hostile relationships, distant relationships, abusive relationships, very close relationships etc. the idea is that the SW can see who in your family you are close to, if you have drifted apart or fight a lot with a particular relative and so on. You can then use it as a base to discuss your family relationships
There's quite a bit online about it, so just look it up and you'll get a list of all the symbols for different relationships plus guidance on drawing it :)