Know the market in your area. First know what area you want to be in then get a good realistic idea of the market or what you can get for your budget. Many buyers tell me their must haves and then I ask them their budget and realize they need another $100,000 to get their must haves. Get a good understanding of what you can get for your budget. Keep an eye on homes on Zillow and Realtor.com to get to know the market and go to open houses. Homes never look the same online as in person. They are either much better or much worse.
Talk to a lender. If you need a loan to purchase a home then talk to 3 local and knowledgeable lenders. Get an idea of how much you can afford and what types of loans are available for how much cash you have to put towards your purchase.
MLS listings emailed to you. Once you know your market & your budget then have a real estate agent set up an automatic search for you in the MLS. The MLS is the system realtors use and pay for to list and search properties. It has the most accurate information on homes for sale. Realtors know all the public record information, the history on the property & local market statistics through the MLS. Often websites like Zillow and Realtor.com can get new listings a day or 2 after agents enter them in the MLS. So, have an automatic search set up for you directly from your local MLS so you get homes emailed automatically as soon as they hit the market or if there is a price reduction.
Know your must haves. Once you get a realistic idea of the market in your area and what you can get for your budget then really think about your must haves. The lower the budget the less must haves you should have. The larger the budget the pickier you can be. It depends on the area but most people can narrow it down to an area (certain school district or within a commute time of a city), minimum # of bedrooms & single family homes only or would a condo or townhouse work. If your budget is higher you can usually add must haves like a garage, minimum of 1 acre, first floor master, etc…
Be decisive. If you really need to find a home in a week you need to be decisive in all ways. Be decisive on the area, choosing a lender, choosing a realtor, determining your must haves and when you tour the home you love then be decisive and make an offer. Most likely if you love the home so do a lot of other people. Great homes sell for full price or can go above asking in this market so get the advice of your realtor and then make the strongest offer you can make.