I am by no means an expert on this topic, but I have been involved in two transactions as a buyer. This is a list of things I feel helped me. Others with more experience will be able to augment my relatively inexperienced view.
First of all, there are a lot of new terms and I remember also feeling overwhelmed.
The first step would be deciding how much you want to spend. This will be a very personal decision, but make sure to take all ownership expenses into consideration. When renting, everything is bundled into your rent payment. These expenses are largely unbundled when you own. Make sure to take not just the mortgage payment into account, but also taxes, insurance, any utilities (water, sewer, garbage) and maintenance, the last of which can vary widely depending on what you purchase.
Once you've decided on what you want to spend, you can work backward to determine your upper price limit.
Next, it is helpful to get prequalified by a lender. You can do this through your credit union and it won't mean that you ultimately need to get a mortgage from them. Prequalification differs from preapproval as there is a level of verification.
Next ask a lender what documentation you should start gathering. It is incredibly helpful to have this ready to go when you are ready to submit for a mortgage. In parallel, you can begin shopping around for a mortgage.
Next, start shopping. Start looking online and after a while, you'll start to understand the market.
It can be helpful to make a list of what you're looking for. This will help you start thinking about must haves vs. nice to haves.
Find a realtor you trust and like because you'll likely be spending a lot of time with them. It may be helpful to interview them a bit before you enter a relationship with them. Understand that once a real estate agent shows you a house, they will consider you their client. Switching realtors after this time can get complicated because the original realtor may ask the next realtor for a share of their commission once a sale is made.
Try to find a realtor that is OK with spending the amount of time necessary to make sure you're comfortable. Ideally this will be someone who doesn't mind showing you houses for months before you make a purchase.
Next, look at as many properties as you possibly can. It can be helpful to look at several in a day. There is simply no substitute for viewing properties in person and imagining yourself in the space. Looking at properties will help you refine your list of desirable property attributes.
When you find a place you like, make an offer. Your realtor can guide you here. Make sure you have someone you trust. Realize that if structured correctly, you'll still have a couple opportunities to back out.
Often times, the realtor will advise putting earnest money down. This is money to show the buyer you intend to purchase the home. Under certain conditions this money is non-refundable if you don't purchase the house.
Once you've put an offer down and the buyer has accepted, then the purchase process begins. It is common to have contingencies in the contract such as subject to inspection and subject to financing. These contingencies mean that if you find something wrong with the house after inspection you can walk away from the deal. Same thing with financing. This is why getting prequalified can be helpful. If the seller knows you've been prequalified, then they'll be less worried about a financing contingency.
Shop around for a mortgage. You can either do this yourself or get the assistance from a mortgage broker. I'm sure there are several on the forums who will be able to weigh in on the best way to get a good mortgage. Keep in mind that it's not just the rate you're interested in. You also want to know that the entity providing the mortgage will be able to close on time.
Inspection: on the two properties I've purchased, I've had inspections on both. Understand that if you're in a hit market, often times people will put in offers with no contingencies, so make sure to ask your realtor about this.
Shop around for insurance. I'm sure there will be several recommendations on the forum for how to do this.
Once your offer is accepted, it's mostly a waiting game until closing if you've done things right. This is one of the reasons you want to have documentation ready to go, because otherwise you'll be scrambling for paperwork, which adds an immense about if stress to an already stressful situation.
At closing, you'll be signing an inordinate amount of documents. Read everything, make sure you understand what you're signing and take your time. It can be helpful to review things ahead of time and ask questions. The escrow agents will not be able to give you advice for the most part.
That's it at a high level. A good realtor can help you through this.
Hope this helps.