I'd suggest the following sequence for you.
1) Talk to a reputable mortgage Broker or banker to get yourself pre approved for financing, if you will be financing your purchase. (If you won't, then obviously skip this step)
2) Talk to one or two reputable real estate brokers in or near the town or neighborhood to which you wish to move. Discuss the features you require in your new home, and also the things you would like to have but don't absolutely need. Discuss the intangibles, i.e. walking distance to public transportation, to schools, to parks and so on. Talk about what you wish to invest, and then let the broker start e mailing you what is available and what is coming to the market.
3) Inventory is tight at this time, so your search may take on the shape of responding when a new listing that fits your needs becomes available. Some new listings may have specified predetermined times available during which they will be shown. Your broker will be able to advise you on a case by case basis.
4) When you see something you really like, DON'T wait and pass it by on the basis that you haven't seen enough inventory. In this market it could be a long time before another suitable property becomes available. DO review other area sales that have closed so that you have a clear idea of values in the neighborhood of the property. Your agent will be able to share that information with you. Then decide what the property is worth to you. DO move forward with purpose and with a competitive offer. DO structure the offer to be as attractive to the seller as possible. Get the property under contract if you can, then proceed with your due diligence to ensure that the property lives up to the promise contained in the listing agent's presentation.
5) There will be a sequence of events over a 4 to 6 week period to finalize everything, and then the house will be yours. Move in and enjoy!
That's the short presentation. If you have specific questions, I'd be happy to answer them for you.
Tom von Zabern