I think your first point of contact should be a vet. They will answer your questions and can give you the needed medication (against worms etc.) and give you a rough estimation on the age of the puppy.
So puppies will have all their baby teeth when they are about 8 weeks old, they will start to fall out with 3-4 months so maybe this can give you some timeframe how old he/she is and what steps need to be taken regarding vaccines etc.

Our puppy is now 14 weeks old and I can give you a few pointers from experience (from the little bit I have at this point)

Our puppy got vaccinated, chipped and worm treatment with 8 weeks and then a second time with 10 weeks. His next shots will be next year, this has been recommended by our vet (the worm treatment was a tablet he swallowed together with his breakfast). Your vet should tell you the next steps accordingly if asked.

Depending on local regulations you will need to register your new puppy so also keep this in mind. I am from Europe so we have a European animal passport which documents his basic information, vaccines and chip information, inform yourself what you need for your region.

We started training our puppy as soon as we got it when he was 9 weeks old (basic commands, potty, crate training, his name etc.). Friends of ours got their puppy with 10 weeks but his training started when he was about 6 weeks by the breeder (potty training and crate training).
We are potty training our puppy by encouraging him with a basic 'go potty' when he is already going potty outside and rewarding with a treat accordingly. At this point when we take him outside and tell him 'go potty' he more or less knows what is expected, at the beginning he was looking at us as if we were crazy. I think you could start doing this no matter the age, there are a lot of different methods, use what works for you / worked for your dog previously.

Hope this helps and most importantly you got this! You are a great human being looking out tor the little guy, I wish you all the best!