My experience with Bloodhounds is relatively short but I have bred and shown AKC registered Beagles for over 20 years. Since there is quite a lot of trimming to be done on a Beagle and that is what I am used to, trimming a bloodhound came fairly easily to me.
We have three Bloodhounds. Two of them have rather heavy coats with a dense undercoat. The other one is shorter and slicker and therefore, easier to handle.
The equipment that you will need is quite minimal. I use a good pair of 42-tooth thinning shears with a serrated blade on one side and a straight blade on the other. You will need a pair of straight scissors. I prefer a rounded tip so that I can safely use them around the eyes. I use a rubber curry comb and a medium blade stripping knife to remove the undercoat.
Basically, I trim the following places:1. The fringe or "feathering" on the rear.I use the thinning shears on the rear to get the coat to lay flat. Every Bloodhound has a natural line on the rear. I use this as a guide and scissor the coat back to meet that line. When the coat is lying down nicely, I use straight scissors to trim the natural line close to the skin. Clean up the line of the loin using the straight scissors. Sometimes the coat looks like lamb's wool after thinning. I especially notice this in the Spring when the undercoat starts to shed. That is where the stripping knife comes in handy. Don't scrape so hard that you abrade the skin. Stripping knives are sharp.
2. The loin area between the abdomen and the back legs.
3. The underline of the abdomen. 4. The fringe or the cowlicks on the sides of the neck. 5. Tip of the tail.
6. Whiskers are optional.
By judiciously stripping all of the loose undercoat out, it will leave a nice clean look.
The same is true for the sides of the neck. I trim the fringe or "seam" on the sides of the neck with the thinning shears. When you get close to the main coat, use the straight scissors to make a good clean line. If your dog has cowlicks, trim them using the thinning shears so that they lay flat.
The tip of the tail often needs attention. Sometimes it grows like a "pinwheel." Using the straight scissors, I trim the hair that sticks out. Trim it into a natural pointed tip - do not round the tip as this will appear unnatural.
Your hound's feet will look better if you trim the excess long fur between the pads. This often helps the appearance of a loose foot. Make sure that the nails are short.
Whiskers are optional. I leave the "eyebrows" on our dogs because if they track or trail, when they put their head down they can't see as well because of the wrinkles. The eyebrows act as "feelers" and help protect the eye from being damaged.
Finally, I use a rubber curry comb to remove the dead coat and bring a sheen to the coat. I finish up with a hound glove.
I would suggest that you practice trimming on a dog that you aren't showing. The secret to using thinning shears at first is to trim slowly. I use a metal comb and back comb the coat. This will bring up any coat that lays down and you have missed. Thinning shears are more forgiving than straight scissors.
If your dog has a dry, problem coat or skin problem, try giving him a product called "In." I use about 8 nuggets a day. It is wonderful for restoring coat to a natural shine. It is great for growing coat on a dog who has had puppies, surgery, etc.
I hope this has been helpful for anyone who doesn't know how to trim and would like to try it. Good luck experimenting with your hounds and happy trimming!