Obviously it depends on how big your instance is, and where you host it.

Up front, you'll have to pay $5-$20-$100 for a domain name.

For a tiny instance like mine, where you have just one or a handful of users, you can get away with a tiny VPS with just 2-4gb of ram. At Digital Ocean that'll cost you $24/month, and at Hetzner Cloud, that'll cost you $4/month. Digital Ocean is nice because they offer managed Kubernetes for free included in the price of their VPSes.

You'll also need some external storage to store photos and database backups like Backblaze B2. But you'll probably use less than 10GB, so it's free. Beyond 10GB, it costs $5/TB/month.

If you're doing a large instance like lemmy.world with 10k users, then you'll need a large server with 32cores, 64 threads, and hundreds of GiB of ram. that will cost you a few thousand dollars up front, and then you'll probably pay around $100 a month in Colocation facility frees, I think.