I too have begun to have an interest in this as well and made a point to visit someone who actually makes crosses etc.
I highly recommend you call your local orchid society and find out where you might do this as close to home as possible. If you can't visit directly, maybe you could get together at your society meeting and ask the questions.
My limited starting knowledge thus far is after you have made your cross/pollination a pod will form which grows on the plant for about 6-8 months (I am speaking cattleya only here). Then before it opens you send it away to be "flasked". You will get flasks back after 1-2 years
with 100 or so baby plants in it.
Then you have to handle those....it can take 7 years before you get a blooming plant!
I have the highest admiration for such patience, and if I decide to do a cross of my own, it will be a most ambitious endeavor for someone as impatient as me.