(I feel like I’m spamming a bit haha)

One of my friends just announced to me that he’s trans (ftm), or well starting to transition a few weeks ago. I’m happy for him and is 100% supporting him all the way. My problem - and it’s nothing to do with him - is that I sometimes forget that. Like in my mind, I’ll sometime still call him by his old name or use the wrong pronoun. I even slipped up a couple times and accidentally referred to him by the wrong pronoun. I apologized immediately and he said “it’s fine. I understand.” But I still feel horrible about. It’s like I’m truing to teach my head to start using and referring to him as a male, but I still find myself slipping.

I’m not sure how I can fix this entirely.

Us trans people understand that people are used to one name and pronouns, so switching can be a little tricky. When I came out to my parents, it took them a while to switch and even then, they still slip sometimes. But I know that they are trying, so I'm happy. I'm sure your friend is also happy that you're trying.
Just keep going. In your mind, repeat his name and pronouns in some sample sentences so your brain will connect them more. When you use the wrong name or pronouns, even if it's just in your mind, correct it. The more you do it, the more you'll get used to it. Slip ups are fine, really. Don't feel bad about them. Again, just make sure you are trying to use the right ones and eventually, slips ups will become more and more rare. Seriously, don't beat yourself up about it. I'm trans and even I slip up for my trans friends sometimes, and even myself!
Also, I don't know about your friend, but for me, it's annoying when people apologize when they slip up. Just correct yourself and move on with what you were saying. The right name and pronouns are a big deal to us, yes, but the apologizing gets old fast.

Imagine it's like your friend has changed their name. Let's say, from Joe to John. The sounds are close to the same, so you'll say the one you're used to. Likewise, he and she are only a letter apart. The sounds are almost identical. If you remind yourself of what to say, you'll eventually use the right pronoun iwithout thinking.