A good way to start, is by going to the ARBA website and seeing if there is a show near you. Attend the show and start talking to people. Observe and have fun! In my opinion, rabbit people are some of the kindest and helpful people I have had the pleasure to meet. Most of them are very willing to answer any questions and can point you in the right direction of some good breeding stock.
How do you improve your herd? By knowing the standard, and then taking that standard and looking at GOOD examples of your breed.
Say for instance you are doing holland lops. Don't look at all the pet quality rabbits out there. Look at what wins on the table and then visit the websites and facebook pages of the people who win on the table. Learn to see what the ARBA standards are calling for. DO NOT be SWAYED by the pet people out there. Seriously... just don't be. For me this year... it's impossible to find decent holland lops unless you know who to look for as there SO MANY NEW BREEDERS. GAH.
Go to the shows and introduce yourself to people who have your breed. Express that you are new and just want to learn. Ask good questions. If you are confused about something the Standard calls for... ask questions, get examples.
Buy what you can afford and DO NOT BE PRESSURED into buying something expensive. Seriously... if you can't afford to lose the money if the bunny unexpectedly dies... then don't buy it. Rabbits die from stress, illness, loud noises, new feed etc. So hedge your bets a little. If you have to buy cheaper and it takes you longer to get where you want... then take that time.
Do note: like BoydsBunnies said... most rabbit people are kind and helpful. Eager to help new people get started. BUT, at least in my neck of the woods, some of the new breeders haven't been exposed to the kindness and helpfulness of us old breeders and haven't learned to temper their words or their expectations. So temper your expectations and be aware that some people...
need more exposure to the kind people of the rabbit world.
How many rabbits do you need to improve your stock... could be as little as one, could be 10 ... could be 50. It might all just take time and patience. You can't give up because one rabbit doesn't perform as well as you want. Sometimes you'll breed rabbits expecting you'll get "x" from rabbit... but you don't get it the first litter.... and might not get it until the fifth litter.
Where to find good breeders... you know what? I'm still learning that.
To actually improve your herd - keep good records. There's a program called 'Kintracks' which is technically a pedigree program, but it also tracks matings, sales, feed, shows, weights, offspring, coefficient of inbreeding, etc., etc. It's also not a very expensive program, it's somewhere around $20 in Australian dollars. It's a free download to start and then you can send in the money to get the key to unlock it further. That one time payment lets you get the updates for the program and if you have an older computer, the program is free. Using that program has done the most to improve the herd here.
To get into showing, go to some shows. Even if you don't take any rabbits to the show, you'll get an idea of what's available in your area. If you see a breed you really like, ask the person showing their rabbits about the rabbits and how to get started. Find a mentor if you can.
I think the ARBA website has different breeders listed. That may be a good place to start. Otherwise, ask here, perhaps. Should you be interested in English angoras, I could perhaps answer some of your questions and I'm sure anyone else with a specific breed would be happy to talk about their bunnies as well.
Once you find a breed you like, look for pedigreed stock. That seems to be a main difference between 'pet' breeders and breeders. Someone who has a couple of pet bunnies and 'ooops' there's baby bunnies doesn't always breed for breed improvement. Someone who is keeping pedigrees and knows which buck met which doe when will have a lot more ability to improve their stock than someone who just lets a few bunnies hang out together and not actually know who the sire of the litter may be.
Also, get the absolute best bucks possible. A buck will be bred with multiple females so he will have a lot more influence on your herd than a doe will. A doe will have a few litters, but she will have less litters than the buck so always get the best bucks. I keep six bucks pretty much all the time. If there's less than four bucks, I'm actively breeding to get more bucks. More than six, though, then there's not any more room for more of them. All the bucks have their own separate space so there's an entire 'buck hutch'. The females can live in groups so they take up less space per bun. There's another big hutch just for the females. Also several 'nesting' hutches which are rat proof. Then several 'grow out' hutches for the babies until they're adult sized. There's usually about two dozen adult buns here, four of them bucks, the rest of them does. Usually about four to six of the does will be actively breeding, the rest of them are 'micro-sheep' making fiber for yarn.
Don't sell off your best offspring. Before listing any of them for sale, look them over carefully and critically and save the best for yourself. If anyone asks, that one is 'already reserved'. If you try to tell them you're keeping it for yourself, they whine and complain and try to talk you out of it. Much easier to either tell them it's already reserved or not even let them see it in the first place.