.How do you reserve? Online only, by phone or combined.

When we make reservations we do online and then by phone ( it's free ) make sure they got it and it's right.

I most frequently use online reservations, at least in preference to phone ones if given the option. Phone works too, though. When actually on the road and making a reservation for a night or two in advance often the phone is easier and more productive.

I have not had difficulties with the quoted prices being incorrect.

Site specific reservations are not generally of great importance to me personally, provided of course I get a site suitable for my equipment. I think particularly irksome are some parks that only do site-specific reservations and so more or less require me to come up with a site number for a park I've never seen before and know little about. Michigan and Minnesota state parks are offenders in this category; if one arrives after hours with no prior reservation, one needs to call from a hotline phone and talk to a central reservation office to make a reservation for that night with someone who usually has no real direct knowledge of the campground, trying to come up with a reasonable site assignment prior to entering the campground and seeing what looks appropriate. On the other hand, if the sites vary and there's reasonable information about them, it can be handy to be able to pick one's preferred site ahead of time.

Online for government parks, on the phone an hour or so before arrival for commercial parks when we are traveling.

We stay mostly in state parks....Washington and Oregon. Always book on line....(way in advance). We can pick our dates and pick our sites...we have favorites.

We don't reserve, but if we did, we'd prefer online reservations. That way you've got a hardcopy (internet style) of the transaction, and there can be no mistake if you show up and something isn't quite right.
Phone calls can miss details and omit things which affect the transaction, at both ends, and unless you record the conversation, you're on your own to prove what was said, and promised, and so on.

As far as pricing quoted being the final price, that's always hit and miss. Websites and phone calls can both omit additional fees and extras which might not be mentioned in either form of reservation. It's one reason why we don't reserve. We just show up and take pot luck. It usually works out for us.