This guide is about the trail itself but written for the beginner. If you're looking for a good guide on backpacking I suggest you start here but I will not be making a lot of assumptions on knowledge, so this guide should be good for everyone.
The Hoh River trail takes you about 17 miles from the Hoh Rain Forest Visitor Center up to Blue Glacier on the north side of Mount Olympus. Check out some pictures at alltrails.com and at the end of this post. There are quite a few camp sites along this trail so you could do it in as little as 3 days 2 nights, or just stay out there an extra day or two and enjoy your time a bit more. It's more about what pace you can handle and if you have time.
For planning purposes you want to take a peak that this map from the NPS.
Take a look at the image above from the NPS map. First thing to notice are the colors of the camp sites. Brown is first come first serve for camp sites but they have overflow on the banks of river, it's not technically limited. The yellow means sites are limited. You can make reservations at the yellow ones but you don't have to. For this part of the Olympics 50% of the sites can be reserved but the other half is first come first serve, you just buy from the Wilderness Information Center up to 24 hours in advance.
Timelines and Reservations
For reservation information visit the WIC.
3 Days 2 Nights
If you're doing a 3 day 2 night trip your best bet is to camp at Lewis Meadow. This means 10 miles day 1, 14 miles day 2, 10 miles day 3. The long second day will be without your tent and most of your food etc. The second day is a longer hike but with most of your gear back at your tent. Don't worry about leaving most of your stuff unattended, no one is going to steal anything and if they do they have to haul it 10 miles back to their car.
4 Days 3 Nights
If you're spending 3 nights out there don't waste 2 nights at the same camp site! Spend your first night at the Olympus Ranger Station or Lewis Meadow, second night at Elk Lake or Glacier Meadows, then back down to the Ranger station or Lewis Meadow. The main thing to keep in mind is that after Lewis Meadow, when you cross the Hoh river, the climb starts to get pretty steep. If you set up camp at Elk lake it means less uphill time with your entire pack on. It's 2.3 miles from Elk Lake to Glacier Meadows and it's a steep 2.3 miles.
More than 3 Nights
If you're spending more than 3 nights up there consider taking a day up to Hoh Lake (see NPS map). It cuts off to the north just after the Olympus station but it's plenty steep. If you're wanting to take it a little easier just remember the hard part is lugging your gear up hill. On the way back down everything is a little easier. Spend more nights on the way up and fewer on the way down if you need to.
Water is everywhere, you're hiking up a river to a glacier. Bring a filter, bring a couple bottles and bring some purification tablets as a backup. As a guideline there is no such thing as stopping too frequently for water on the way up because you're not sure where the next source will be. That being said, it's not enough of a concern to dedicate a lot of thought to, just make sure you can filter it when you find it.
Every camp listed on that map has a pit toilet except Happy Four and Martin Creek. If you're heading out onto Mount Olympus you have to use a blue bag. If you can't hold it and you're on the trail, use a trowel and bury it 6-8″ deep and 200 feet away from water. If the thought of dropping a deuce in hole in the ground is scary, read this.
With the exception of Martin Creek each camp on the trail has bear wire. You do not need a bear canister if you're camping at any of those sites. The bear wire is pretty easy to use, just make sure you have some kind of separate bag that can hold all your scented items or food. There will be signs at the sites pointing you to the wires.