In building your ice rink, you need to consider many things. Location is probably the most important. Size will be determined by location. How much material you need is determined by size.
When I determined where my ice surface would finally be, I selected a fairly level looking area in our yard between two trees. The trees are about 30-35 feet apart from each other, that limited my width to 25 feet so there would be room to go around the frame of the rink. The length of my rink was limited by the slope of the ground. The ground rises 3-4 inches very quickly after a depression of 35', so if I built larger, I'd have to fill the tarp more.
Here's a list of things to think about when you're selecting your location:
Immovable obstacles (things like trees)
Slope/grade of the yard
Distance from a water source (a long hose requires more work)
Traffic - things like side walks or normal paths for your family to walk.
Location of underground lines (You MUST secure your frame!)
After you've selected a location, then you should determine how large you want to build your ice surface. If you cover more area of your yard, you'll need more materials. However, you'll get greater enjoyment from the ice if you don't have to turn all the time or if there's space for 4 or 5 people to skate without bumping into each oIther.
Once you have your size determined, it's time to start thinking about materials. You'll need a frame, things to secure it, and a tarp to hold the water in. If your base is extremely level (like a concrete surface), then you can use a frame that's smaller in height.
Construction grade pine is the natural choice for most people to use, as it's the cheapest and strong enough. You can use other materials to build a frame, but things like bricks tend to be harder to work with.
I started building using 2x4x10's. I used 2-4 ft sections of 2x4 to secure the 10' lengths. As good as an idea this seems to be, the 2x4s proved quickly after I started adding water to be way too small. On the deepest side, I had to build a brick retaining wall to help keep the water in.
After talking to elgoodbill (who has done this successfully several times), I found he uses 2x10s, 2x8s, and 2x12s. The frame consists of two layers. The 2x12 layer on the outside, and the 2x10s and 2x8s on the inside. This provides about 18" of height on the inside of the frame for your tarp.
The frame *has* to be secure. Not because it may blow away, but because water is heavy. If the frame is not secure, it will bow out and your tarp will fall below the water line and you will lose your water. This is especially bad if it had started to freeze.
I used a a few 2x2s cut to an angle to secure the frame, but elgoodbill suggested using rebar. It would go into the ground easier, be just as secure, and be easier to remove. Plus, you don't have a big square hole in the ground to deal with.
When using 2x4s, I normally use 3" screws. For every place there is to be a screw, I predrill a pilot hole. Even after I predrilled for the screw, I still managed to overload the internal circuit breaker on the power screw driver several times.
If using 2x12s, 2x10s, and 2x8s, you may have to figure out what to use to join them. It would be best if you staggered the joints between the two layers as best you can. (Use a 2x12x12' then use 8' lengths of the other lumber. Your joints will fall in about the center of the other layer.)
You want the inside of the frame to be relatively smooth because if your put a hole in the tarp there, it's the end of it. If something is rough, take the time to sand it smooth or cut it off. There should be nothing on the inside of the frame sticking out.
If you build your frame in place or in movable sections, you won't have to rope a bunch of people in to helping move your frame. The 2x12 is heavy enough, especially if you use pretreated lumber.
To determine what size tarp you need, add 5 to 10' to the dimensions. This is the minimum size of tarp you need. Some tarps come hemmed, and are *not* what they're advertised as. A 30'x40' tarp may be 28' by 39'. Instead of having 2 1/2' on each side of the frame, you'll only have 1 1/2'. If you have a large deep section, you may run out of tarp.
When selecting a tarp, don't think that you can get two smaller tarps and join them together. It most likely will *not* work. I tried that, and never could get a good seal between the plastic sheeting I used. Buy a tarp that's big enough in the first place.
If you get a tarp that's hemmed and grometted, you can secure it on the ground by using tent pegs. Some pegs are too large to fit into a grommet, so you may need a different size.
Once your frame is built, and tarp purchased, make sure your base is clean of things that can rip the tarp (such as black walnuts) and any tools you used. If you're worried about your tarp, you can use plastic sheeting to provide a layer of protection under the tarp. If it's not holding any water, you can use two smaller sheets under the tarp.
Wait to put the tarp out until you're ready to add water. Your tarp shouldn't be exposed to possible extreme weather conditions while you wait for freezing temperatures. (I'm sure it has hailed in december in most areas.) You may want to make sure it would fit before keeping it past a store's return date.
Watch the weather for a strech of below freezing days and nights. This is your best bet to keep leaves out. Put the tarp on the frame, and try to get it as smooth as you can. If you go through the ice with skates on, you don't want to slice a ridge sticking up on the tarp. You may have to use the weight of water to help keep the tarp smooth.
When you start to fill, you'll start to see where the deep areas are. Water will collect there first. Keep your eye on the tarp and make sure no ridges come up from the movement of the tarp. At this time, you shouldn't have secured the tarp to the ground because it needs to move in to the crevices in the ground.
After the tarp is filled enough that it won't need to move too much more, you can secure it to the ground. If you kept the ridges out, you shouldn't have to do much of anything else at this point. Just secure the ends of the tarp into the ground. Don't pull the tarp really tight, as you just put unneeded stress on it. Allow it to move a bit.
You're done filling after the water has reached a minimum depth of 3-4 inches in ALL places. If you add more water than that, all it will do is take a bit longer to freeze. If you can't skate because of thin ice, the extra time to freeze is well worth it.
While you're waiting for the ice to freeze solidly, don't test it with your weight. If you look into the ice, you can sometimes tell how much is frozen. The one advantage of the frame I had was that I could just tap the tarp and see how much water was frozen. If the tarp moved, it wasn't frozen.
After your ice is frozen solidly and ready to skate on, enjoy! You'll want to check the maintenance section while you wait for the ice to freeze.