It seems a lot of newbie beaver trappers have a hard time with footholds. This is the way I do it. I know some will disagree with some things I'll post, that's fine, but this has worked very well for me. Although the below set is a castor mound, I use the same trap placement and strategy at most foothold sets.
I like to find a hump or point that is easily seen by passing beaver. The nice thing about beaver is you can usually make the set where you want to catch them. In other words, you can make the set and lure the beaver to where it best fits what you want/need to do. I like to make the set where there is brown grass so my mud shows up well. Although it's the lure that's most important and your main attractor, I think eye appeal can also be important, especially if the wind is blowing the wrong way. Another thing I look for when setting footholds is the right slope on the bank and water deep enough to drown.
This is the same spot as the above picture with the finished set. The trap is PAINTED WHITE FOR PICTURE REASONS ONLY. If possible, I like to set my footholds (except TS85's) in 1" of water with shallow water in front of the trap as well. By doing this, I know the beaver will have it's feet down and walking when it hits my trap. This is especially important when using smaller traps (like #3's and #4's) because it gives me the best chance of getting a front foot which I prefer. With the drowning methods I use, any beaver that put's it's front foot in my trap is done. Another reason I set my footholds shallow is because when I used to set deep I was missing the occasional beaver, they would just step over the trap. Especially in the spring when trapping travelers, I only have one chance to catch the beaver or it's gone. Beaver would occasionally step over my trap on approach to my set, and swim over the trap when leaving. I knew this was happening because my bait would be gone or the mound ripped up and the trap would still be set. It didn't happen much, but it would occasionally happen. By setting shallow, I have chances at both front and back feet on approach, and both front and back feet when leaving. 100% chance of it stepping in my trap. Traps set deeper also have a better chance of being sprung by the chest, especially if the beaver is gathering mud to carry to the mound. If a foothold set is such that I can't find a shallow spot to set or can't make one, I'll set a 750 or TS 85 in at least 5" of water an elbows length away (about 18-20") from where I expect the beaver to hit it's chest on the bottom when it approaches the bank. I use guide sticks just like when setting shallow (explained in next paragraph), just farther out.
Another very important thing I do, especially with the smaller traps, are the two pink colored guide sticks in the front. At 14" apart, these guide the beaver's feet right in line with where you want them which is right between the jaws so the trap "suitcases" the feet. I'm convinced one of the main reasons for sprung, empty traps is because the beaver has it's rear foot on a jaw when the trap fires. It's very hard to get a good hold when this happens. Especially with smaller traps, the closer you can get the rear foot to right between the jaws and the center of your trap, the better off you will be. Set your trap so the outside jaw is right against one of the guide sticks, off-setting the pan 4" - 4 1/2". Traps set closer to center will only ask for marginal holds. If you measure a large beaver's width between the legs, you will see they are wide animals.
I prefer the 7 1/2" jawspread traps, like MB 750's and CDR's. They are a lot more forgiving of bad trap placement than the 6 1/2" (#3 or #4) jawspread traps. 750's and CDR's aren't legal everywhere though. #3 and #4 sized traps should ALWAYS be 4 coiled VERY strong. You can't get traps too strong for beaver. Make them as strong as you can set them. When they start to get weak, replace the springs. One lost beaver would have paid for a lot of replacement springs.
Pan tension should be at 4-5 pounds to get a better hold and avoid muskrats.
The trap dog should be at 3:00 or 9:00, depending on what side you have your trap set on, with the dog to the outside. Stabilize your trap, so it's not rocking, with small sticks or rocks under the jaws and levers.
When not in current, I like to dig the traps down so the pan is level with the bottom. If you do it in current, sand can wash underneath the pan.
I like to use lot's of the blackest mud I can find on my mounds for eye appeal. If there are some freshly peeled sticks in the area, I throw those up there too. I know eye appeal is important and useful, because often I'll catch beaver on both sides of a river or creek in the same night even when the wind is blowing hard from a certain direction. One of these years I'm going to try not using any lure on some sets just to prove this point. I also use a stick of popple at most sets. It's optional though. At least here, popple is candy, and can help in attracting up to the bank. All beaver don't go to the top of the mound. Especially smaller beaver, like 2-year-olds, sometimes will just go near the edge, get a whiff, and leave. Bait helps get them to commit.
Notice the blocking around the set in the above picture. Blocking can be very important. Sometimes beaver will try to go directly into the wind to your lure or just try to go around for some reason. Make the way over your trap the easiest route to the mound. Dead tree tops and brush tops laid sideways work well for blocking. If you have beaver that have been trapped hard before, a lot of blocking may put them on alert, although I have rarely seen this be the case. If I know I'm after possible smart beaver though, I'll make a small trench at the base of the mound with my boot and use a little grass to try to block off the sides best I can, without making it look too obvious and hope for the best.
IMO quick drowning is very important, especially with smaller traps. I know there are good trappers that don't drown their beaver and I admit it's not always necessary with 7 1/2" jawspread traps and in some situations. But with #3 and #4 sized traps it's necessary. I've always said a dead beaver on the end of a drowner isn't going anywhere, a live beaver still has a chance. The end of the drowner preferably should be in 4' of water or more. It's 4' from the nose to the drowner on a large beaver. With hind foot catches with the smaller traps, you want that beaver under water as soon as possible. Beaver can live a long time with just their nose sticking out of the water. You can get by with less water with larger traps, but I personally seldom set a foothold with less than 3 feet of water to drown.
Drowning rods make life much easier for a beaver trapper. I like 1/2" rebar or stock rod, 10' long on average. Some are 12' and a few are 8', but 10' get's me into deep enough water to drown in most of my set locations. Just stick the rod into the mud as far as you can push it, stake with a 24"-36", 1/2" rebar stake and you're through. I've never had one pulled out. The only problem with rods is they can be hard to get into a rocky or hard bottom. They're not for every situation. MTP sells a kit called the "Bauer no-weld" system if you don't want to make your own locks or have access to a welder. All you need is the rebar and the kit.
I use weights with cable (usually 1/8") or #11 soft wire where theft might be a problem or I can't get a drowning rod into the bottom. I consider 45-50 pounds about right. You can get by with less on softer bottoms. Any less weight and you run the risk of the beaver getting slack in your cable or wire and not having the drowning lock slide properly or at all. The above weights were made from concrete test cylinders filled with concrete and rebar for a handle. 50 pounds carries easily this way. 6" plastic pipe, 12" high, would also work instead of the test cylinders. The blunt edges on the top dig into the bottom nicely. Others use feed sacks filled with rocks or sand at the trap site. For those far back places though, I just use 3"-4" saplings for stakes cut at the site. They must be the kind that beaver won't eat though.
I like my homemade "L" drowning locks. Swivels work too, but the holes are too small to suit me. The bigger holes I have in my "L" locks are big enough that they will slide easily past any twists or kinks I may get in my cable or wire.