And you also probably already know about safety or you wouldn't still
be alive or have all your eyes, fingers, etc.
But just to be sure I'll say it anyway:
BE CAREFUL AND THINK!
In the past I always placed both anvils up-side-down. This way the "hit" on the top anvil was on it's working surface which seemed to make sense and is the way I first learned to do it. But I've since learned that many others place the two anvil bases together (Top anvil is right side up.). I believe the purpose of this is twofold. First, the base of the "flyer" is generally a larger surface for the explosion pressure to act on, thereby imparting a greater impulse. In addition, if the flyer has a base cavity like the bottom anvil, you can fill it with powder as well (using tape or some other method to hold the powder in) in order to get more energy.
The bottom anvil should be the same weight or greater than the top anvil and be placed on a very solid surface or, like I do, on a big, thick metal plate. (I've got a one foot square, two inch thick aluminum plate.) The mass and surface area of the large anvil and backup plate combination is very important for getting maximum height from the top anvil or "flyer". There are two reasons for this. First, the conservation of momentum principal (basically Newton's third law) implies that, with a given top anvil mass, increasing the mass of the bottom anvil will increase the top anvil velocity (at least initially) and lower the bottom anvil (reaction) velocity. Since the ENERGY inparted to each anvil is proportional to the SQUARE of it's velocity, the "flyer" gets lots of energy fast as you make the bottom anvil bigger and the final altitude of the "flyer" is directly proportional to it's energy. Second, what we have here is basically a cannon with a zero length barrel. As soon as the two anvils separate even a fraction of an inch, the pressure is quickly released and it's basically ballistic from there on. So you don't want the bottom anvil to move any more than possible. Mass and "footprint" make this happen.
I like to "point" the anvil just a bit off from vertical. I don't want the "flyer" to come down on my bottom anvil.
Along the same lines as the above discussion is the subject of which powder to use. First of all, it should only be black powder. This is traditional and looks great because of the large cloud of dense white smoke. Also, smokeless powder would probably be very dangerous due to higher pressures. I've never heard of anyone using it and would never try. Given that, which black powder to use? Well, the idea seems to be to use the fastest burning powder you can get. This is for the same reason as mentioned above. You need to get the job done asap since as soon as the two anvils separate, the pressure is released and the "flyer" is on it's own. In black powder, this means the smaller grain size. FFFFg powder is very fine grained and used typically for the pan of flintlock muskets, etc. It can be hard to find. I have always used FFFg powder. This is still fast burning and very commonly available. If the cavity in your anvil is pretty small, it might be worth getting the FFFFg powder to get the most from the smaller volume.
The charge is usually put in the cavity which was often present in the base of the old forged anvils. This cavity was generally a product of the manufacturing process and was there to allow easier manipulation during forging. It may have also been used sometimes to accept a spike driven into the anvil support to help keep it from walking around while work was being done. It is really important that the bottom anvil be a very high quality forged anvil. I have an old Peter Wright anvil made probably around the turn of the century. Many new as well as older anvils are simply cast iron and quite brittle. The high pressure from the black powder explosion could shatter these anvils tossing chunks of cast iron around the area at high speed. VERY DANGEROUS. You should also make sure the anvil doesn't have any cracks. If it rings nicely when struck, it is probably ok but inspect it before every firing. I think it is also very important to never use any components in the firing which could turn into projectiles like metal gaskets, etc.
I believe that traditionally, the anvils were lit using either a fuse of some kind, or a powder trail and forge heated iron rod. The later seems very risky as you are way too close to the "action". When a fuse was used, it was usually laid on the bottom anvil and a gasket and spacer was built up around it so the top anvil could be put in place without crushing the fuse and at the same time sealing the gap created by the fuse thickness. Sometimes a groove was ground in the base of the anvil just deep enough for the fuse. I think this would work much better but I didn't try it. I tried the first fuse method some with not very good results. So I drilled a hole for the fuse through the bottom anvil base into the powder cavity. This works great and allows me to use a single thin gasket (a playing card is traditional).
After the bottom anvil is placed up-side-down on the ground or backup plate I slip the fuse in so it extends a quarter inch or so into the cavity. Then fill the cavity with powder, place the gasket on top (after making sure all grains are brushed away from the anvil base) and then carefully place the top anvil over the cavity. You should beforehand have found the center of ballance of the top anvil and made marks on both anvils to allow easy centering of the top anvil over the cavity. If the top anvil is not ballanced over the cavity, energy will be lost in rotation of the anvil instead of altitude. I like to first touch the two anvils together at the farthest point from the powder just in case there is some static electricity built up between the two.
Stats of my anvil setup: