I bought my first home just under 2 years ago. It was a daunting process, but here are the steps I followed:
1. Saved money for down payment (assuming this was done by now).
2. Found a mortgage lender I was comfortable with and planned my budget. Try banks and brokers - get recommendations from friends/co-workers. You need to trust this person has your best interest in mind. I did this about a month before I started seriously looking for houses. Another thing I found out, when I first started out, my price range was much lower than where I ended up, as I learned about how the tax advantages allowed me to modify my W-4 allowances. I also created a spreadsheet where I listed out every expense I could think of - from estimated mortgage payment, to utility bills, to recreational stuff I wanted to continue doing. I used that spreadsheet to determine whether or not I could afford the place I chose over the long haul.
3. Got a Buyer Agent - in my area, I found some exclusive buyer agents that I interviewed. This was a fantastic decision for me. Mine was recommended by my mortgage broker. My agent helped point out things to look for when evaluating a house - pipes, foundation, structural things, etc. He pointed out maintenance items he saw that might be problems for me that I would never have thought of.
(One tip I got from my mortgage broker is to make sure if you are working with an agent, that they communicate/work with the mortgage broker - makes the closing work so much smoother)
4. Look for houses - review houses your agent finds (if you go with an agent), and do your own web searches. Consider the neighborhood - crime, schools, city/rural. Know what you want in a house - your "needs" vs "wants". I found out through the process some of my needs and wants changed. Example - I was never a fan of hardwood floors, but the house I ended up with - I actually chose because of the hardwood floors (they were a different type of hardwood floor than most of the houses, more modern looking and just "worked" for me). Be prepared for this shift - as you start getting into the houses, you'll start to find there are certain things you keep looking for first. Pay attention to those things, as those are most likely your real "needs". For me - it was the kitchen - if the house didn't have a kitchen layout I felt comfortable with, it was a deal breaker.
5. When you start finding house candidates - use local websites to look up utility costs and taxes - keep in mind, most mortgage payments include property tax payments. Your mortgage may be within budget, but will it still be after you add in the taxes. Doing these look-ups you may find you can afford more "house" in different areas, due to tax rates levied - some areas have lower property taxes than others.
6. Choose your house. My buyer agent told me when a person finds their house, it's like finding a spouse - you just "know" when you see it. I didn't believe that at first and spent about 2 months going out multiple times a week looking at house after house. Toward the end, I had narrowed it down to 2 candidates, and was planning to pick one of the two, but I wasn't 100% thrilled with either one. Then a couple days before my last viewings of those houses, I did one more search on my own, and the house I'm in now popped up. As soon as I saw it online, I knew that was the house for me. The minute I stepped inside during the viewing, it felt like I had lived in the house for years. Keep this in mind - particularly if you are planning to stay in the house for a while. If not, and are planning to move out in a few years, probably a "close enough" would do just nicely.
7. Place the offer - this can be a nerve wracking process. Your offer could be accepted, countered or rejected. I had a friend who was house hunting at the same time as me and he had 2 offers that ended up being rejected. It was hard mentally to go back out again to keep searching. He finally got his on the 3rd try. I was super lucky and got mine after one volley of a counter offer - first try. Just be prepared for this - don't get too attached to the house in case the offer falls through. You'll be surprised how much you were hoping for it if you do experience an offer rejection.
8. After offer accepted - this is the point where it becomes fun - time to finalize your mortgage papers with the actuals, get a good house inspector, get a good appraiser (typically mortgage lenders will do this for you), set the closing date. After you now know where you will live - start anticipating what maintenance items you may need now that you are a home owner (lawn mower, snow blower, ladders, other gardening, other tools for indoor maintenance, etc).
9. Attend the closing - I've heard these can go 2 ways. My mortgage broker made it easy - he had me sign everything before the closing, then at the closing I just had a few extras to sign and sit and wait for the paperwork to be settled. Others can be like a whirlwind if you have to sign everything at the closing. I heard typical closings are only an hour, and there is a ton of paperwork to sign. If you know you will be signing at the closing - I'd recommend seeing if your mortgage lender can go over what each of the papers mean before the closing so you don't freak out at the closing - you may literally feel like you are signing your life away and be shell shocked after your leave. Once the paperwork is done - you get the keys from the previous owners...if you have the chance, ask for any quirks about the house they are aware of...then go to a restaurant to celebrate!
10. Move in!
Hopefully this is helpful for some.