I think things should go something like this:
1. Check your credit. If there are any issues, fix them before you start trying to get approved for a mortgage.
2. If your credit's OK, get prequalified for a mortgage (this is where you tell the bank your info and they give you a prequalification letter based on what you told them; a preapproval means they actually pull your info instead of just trusting you...since this involves a hit to your credit, it's best to get preapproved/approved just once).
3. Use your prequal amount to help you start narrowing down your search for houses. Note that you will get preapproved for a surprisingly high number. Just because the bank wants to give you a mortgage for $400K (for example) doesn't mean that's what you have to spend. Conventional wisdom says you can afford a mortgage 3x your annual salary (this assumes you have other debts, like a car payment and student loans).
4. Consider where you want to be, as well as things you NEED and WANT in a dwelling. I (and most other women on this board) believe that location is most important, because it's one of a very few things that you can't change. For example, we decided we needed the right neighborhood, a garage, a fenced yard for the dogs, less than $200K, and laundry in the house. We wanted at least two stories (i.e. not ranch), 3 bedrooms, minor fixer-upper, historic character, no major issues, new roof, etc. We knew we could compromise on the second list, but not the first.
5. Go to a few open houses. We went to several in our neighborhood and it gave us a good idea of what was available.
6. Get an agent. Ask friends for recommendations. If you don't get any good ones, check Trulia. We looked at the Columbus, OH boards on Trulia and contacted the agent who had answered the most questions. We had a response from him within an hour and he was a delight to work with. Your agent can set up an e-mail listing for you; he/she will get criteria from you (neighborhood, price, # of bedrooms, etc) and you will get automatic updates from the MLS daily of houses that meet your criteria. Your agent will be able to guide you from this point on.
6. Seeing houses with your agent: when working with an agent, remember that he/she is super busy! We found that we liked to take the reins a bit, so we made lists of houses we wanted to see. Before telling our agent, we drove past them and attended open houses if possible. We were able to rule out some of them by doing this. Then we sent a list to the agent with the remaining houses...each one of these was a house we thought we could buy. By doing this, we saved ourselves and our agent a lot of time. We only ended up going out looking twice; each time we found a house to offer on (the first offer fell through).
7. Good luck! Check these boards often; a lot of ladies here have tons of great advice and are happy to help.