Buying a property in the US for the first time…

Varies by state and, in some states, by county. Buying in Fairfield County CT was very different than Florida.  

Where are you?

You can get a cheap house if it’s distressed and your willing to work on it.

Assuming you are financing or looking to get a mortgage, the first step would be to get preapproval to see what you qualify for. 
Next step, you could search for a trusted real estate agent, and real estate attorney.
The agent will guide you through the entire process, but you’ll want to have that preapproval letter before you even start looking, to save time.
A real estate agent is not required, especially if you are buying directly from an individual, in that case you can use an attorney only. However, if you plan on looking at houses and making offers an agent can help with that and can often speed up the process.  Keep in mind that an agent will usually want you to sign a contract, and you will be obligated to compensate them for their time, usually a percentage of the purchase price. That part is usually negotiable, but not all agents will allow you to negotiate their fee structure. 

I dunno why so many comments are getting downvoted lol, but I’ll give you my advice. Pretty general since you don’t give any details of what kind of property you want… but here goes.

Find a local agent with experience in the area you are looking for. You will probably be asked to sign a representation agreement with them. Sometimes, these are super long contracts. Don’t sign a long contract with someone you don’t know. Say you’ll sign for 30 days and if the person is a good fit for you, then you can renew it monthly.

Watch for a fee in that contract often $495, that you are going to be asked to pay on top of any commission baked into the house price. Tell the agent you are not willing to pay that, the seller should pay their commission. If you protest it, it will go away. If not find a different agent.

Then go look at as many houses as you can. If things are selling fast in your area, you might feel rushed, but please still take your time. Right now IS the busiest selling season because many people want to move before school starts in the late summer/fall. But people are always selling, and you won’t have as much competition in the fall once the school-schedule-sensitive buyers are gone. Looking at a lot of houses is very educational, you will learn a lot. If you see a house, don’t bid on it, and see what it sells for, that is valuable data. Although know that initial contracted prices are often dropped after someone gets an inspection, and finds things wrong with the property.

Speaking of inspections, get an inspector YOU select and hire, not one your agent recommends.

No idea what contracts are like in the UK… but here buyers normally make an offer to buy, that is contingent upon an inspection period, and, sometimes upon your ability to obtain financing. You will post an earnest money deposit. The inspection contingency period is usually 7-10 days. If you find a deal breaker in that time, your agent will send over a cancellation and you’ll get your earnest money refunded. If you back out after that contingency expires, you will forfeit your earnest money.

If you are getting a loan, you also want an appraisal contingency. The lender will do a valuation on the house, and as long as it’s not overpriced, they’ll agree to make a loan. If it is overpriced (in the lenders’ eyes which may not be wearing appropriate glasses) then they won’t make a loan. This is another reason to cancel and get your earnest money back. You say you are paying cash but just an FYI.

Also go do some reading in the FAQ in the sidebar. Good luck.