What country are you in? It might matter.

Assuming you are in the US, the process is lengthy and there's a lot of hurry up and wait, but it's not too bad.

• First you save up your down payment which can be as low as 3% of the purchase price (or even lower for some people, many vets pay 0% down). 20% or higher will get you a lower payment because you don't have to buy insurance for the bank and may get you better rates.
• Next pick a lender either by manually calling around to a bunch of banks and seeing what they offer or by going through a mortgage broker who gets paid by the bank for bringing them business. When you have picked your bank you want to get pre-approval for the amount of money you wish to borrow.
• Contact a real estate agent who works for buyers. Recommendations from friends and family help a lot here. Broadly you want somebody with a lot of experience who helps a lot of people buy homes. You generally don't want your cousin's friend's barber who's starting up real estate as a side gig.
• Your real estate agent helps guide you through the local market practices. You tour houses and if you find one you like your real estate agent helps put in the offer which will likely include a payment of earnest money which you will lose if you pull out of the contract.
• If the offer is accepted you and your agent negotiate the purchase agreement with the seller including any contingencies such as passing a home inspection.
• You sign a bunch of papers with the bank, nowadays probably on a website. The title company does their work including writing a title insurance policy. This stage takes about a month.
• When everything is already you will sign the final papers and get the keys.
• After a month or two your bank will inevitably package your mortgage into a bond which is sold to one of the hilariously evil and predatory mortgage-backed security companies that are still doing the same shit they were when they ruined the world economy 15 years ago.
• Budget roughly 1-3% of the home's value in savings per year to pay for maintenance and repairs.

Edit, addendum: hire your own lawyer to review the contracts. This will cost about $1,000. If you don't already have a lawyer you can contact your state bar association to find one that is relevant to your needs. Don't buy a home as co-owner with a person to whom you are not married. If you must, you will need your lawyer again to draft up a full partnership agreement that describes how to divide the asset in the event of death, disinterest, disability, disloyalty, etc. You don't want to be half owner of a house with your deceased girlfriend's parents who want to sell it out from under you. Pick a number as your budget and stick to it. The temptation to get a house that is a little bit nicer will always be there. This is how stupid decisions are made.