How do I handle the logistics of freelance web design?

I am friends with a freelance web designer, and I believe he does a mix of these two things, depending mostly on his client's technical prowess. For less tech-savvy clients, he sets everything up, and charges them an upfront fee plus annual maintenance (to pay for the renewal fees plus his time, and he makes tweaks as needed).

I recommend marketing your business (yourself) as a full-service web shop: set everything up (domain, hosting, etc.) for your client and invoice them. In general, people just want the easiest solution possible. Register domains under your client's name if possible (less hassle down the road should they want to transfer, etc). Strongly consider purchasing quality web hosting and becoming a "reseller" to your clients. Reselling web hosting is a great way to get higher quality web hosting for a lower cost (for both you and your clients). Bonus in this approach is your business-client relationship is automatically maintained on some level (even if it is just the client paying you every month). It also gives you a chance to provide courtesy check-ins with your client, further solidifying the relationship. It's a bit more work, but the working relationship you build with your client is well worth it.

If you'd like, you can always make exceptions for clients that wish to maintain their own domains, hosting, etc.