Firstly, and I cannot stress this enough, discuss this with your vet first. And if you don’t have one, get one now. Googling (and posting questions!) is not a substitute. It’s much easier and safer to prevent issues than solve them later.
You say the kitten is a few weeks old, though judging by your previous post it sounds like they are old enough to be independent (~10+ weeks). Just in case it's relevant, there is a big difference week to week in a kitten’s early life in what’s required for kitten care. A four week old kitten is going to need a lot of care and attention and an eight week old kitten will be more mobile and independent (but still need attention!). Kitten Lady has some great resources on determine age and care at various growth stages.
If after reading through what is going to be required of you, you think you’re up for this, and your vet has approved taking the kitten home, start with your kitten in another room, separate from your cat. Sanitize whatever is in that room before they get there and wear clean clothes whenever you engage with the unvaccinated kitten. Do not allow the kitten to share water or food bowls, litter boxes, blankets, etc with your other cat. Separate means separate. This phase could last weeks; it will be up to the discretion of your vet.
When the kitten has had their first round of core vaccines and the vet has approved it, then you can begin slow kitten/cat introductions. Jackson Galaxy has lots of resources on how to slowly and safely introduce cats.