Eh, bathing dogs just isn’t that big a deal, especially if you have a sprayer attachment or it’s warm enough to turn the hose on them in the back yard. If you don’t have one of those things, it’s probably worth spending the money to go to a self-serve dog wash, where you pay a small fee for the use of their elevated tub and sprayer hose.
Since you’ve not done this before, I’ll give a few tips from my years in the vet world. First, if you’re going to trim the nails, clean the ears, or express the anal glands, do it before the bath. It’s easier to handle a dry dog than a wet one, and any unpleasant smells can be shampooed away. Take a couple of cotton balls and stick them down into the ear canals to prevent water/soap getting down in the ears and potentially starting ear infections–this is especially important for dogs with heavy floppy ears that are prone to infections anyway, like your hound breeds.
Always, always, always test your water temperature before putting it on the dog–it should be barely warmer than skin temp. Colder than that is going to be uncomfortable for both of you, and warmer than that can dry doggie’s skin out. Always, always, always use dog shampoo, not people shampoo or dish detergent for routine baths. Human shampoo and detergent tend to strip too much oil out of the coat and cause dry skin.
So, you have your nails/ears/butt done, your cotton balls in, your doggie shampoo at hand, and your water temperature tested. Start wetting the dog, starting at the neck and working down the topline (basically, the dog’s spine) to the tail, then working your way down the dog’s body and legs, getting the head last. Be sure you tilt the head back when wetting or washing it, to prevent getting soap or water in the eyes. When the dog is thoroughly wet, apply shampoo to the topline and start scrubbing just like you would wash your own hair, working the soap down the body. Most dog shampoo is fairly thick, so add a little water periodically and keep spreading. Use more shampoo as needed.
Rinse in the same pattern that you wetted the dog down, and rinse until the water runs clear. When you get done washing, squeegee the dog down with your hands. You’ll need far fewer towels that way, and reduce your risk of getting huge slops of water shaken in your face.
With patience, you can teach them bath-time commands like “up” or “turn” or “paw” to get them to get into the tub, turn around so you can wet/scrub/rinse their other side, or give you their paws to be washed or dried off.