How to start going to the gym at 35 years old?

Start with light weights and basic exercises to learn proper technique - that's the most important thing at any age, that's what I'd do in your place. It's best to hire a trainer for at least a couple of sessions so they can show you how to work with each machine, otherwise you can mess up your back later.

I'll add that at 35 your body recovers slower, so don't rush to gain weight week after week.

People above already correctly mentioned technique and a trainer - that'll really save you time and protect you from injuries. I'd also recommend finding a stable training schedule and sticking with it for at least three months before changing your program - your body adapts slower, but the adaptation lasts longer.

How long has it been since you've done any sports at all?

I got back to the gym at this age myself after a few years off, and I can tell you - the main thing is not to overestimate what you're capable of in that first month. Psychologically it feels like if you used to work out or you're young at heart, you can jump right into decent weights. That's a dangerous misconception. I knew a guy who on his third session decided to "relive the glory days" and threw out his back doing squats. Couldn't do normal household chores for two months after that. So the first two weeks - keep the weights really light, even if it feels silly. You need to give your body time to adapt and learn the proper form. A trainer for the first few sessions - that's not a luxury, that's an investment in your health.

The second thing that everyone seems to forget to mention - recovery after 35 takes more attention. A rest day between heavy workouts helps me, enough sleep and decent nutrition. In the first month I didn't notice any muscle gains at all, then over three months the results started coming good. You don't expect miracles in a week, and then you don't get disappointed. The main thing is consistency, not intensity.