There are dozens of different shield styles that were used in the middle ages and each was effective in the context it was intended for.
Choosing your shield
Pros and cons of the three most popular shield styles.
1. Heater. This is the classic "shield" shape, which is basically a square with a triangle stuck to the bottom, and it usually is strapped to your arm. It's fast, stable, and covers you pretty well, and tends to be a good choice for fighters who focus on speed, mobility, and precision. It's not the best form for fighting in close, and can leave your sword side more exposed than some other styles.
2. Round. Round shields usually are held by a handle in the center and are especially favored by fighters with Norse personas, which we have a lot of here. They are good for fighting close in and shutting off you opponent's attack while hiding your own. They are also wider than other shield styles, which helps against attacks coming in from angles. The weakness is that it can't cover low and high at the same time, so you have to do a lot more sword blocking. They are also easy to tip out of position, and can be hard to hold up after a while.
3. Scutum. This is a rectangular shield, held from a handle in the center, and is a nice compromise between heater and round, with some of the strengths and weaknesses of both.
Construction
I suggest building your first shield out of plywood. 1/2" exterior grade should be sufficient. It should last just long enough for you to figure out what you want to do differently next time.
1. If your shield is center held, get a shield boss. You can order a basic one online for about $20.
2. Measure. For heaters and scutums, the width should be equal to the widest point of your shoulders, and height should be from chin to crotch sitting on a bench. (For women you might increase these by about 10-15% to get a similar proportion.) For round shield diameter, I recommend measuring from elbow to elbow with your fist in your palm, though you can go fist to fist if you have short arms.
3. Cut it out.
4. Attach some edging. A nice way to do this is to hot glue some rope along the edge of the shield, then cover with garden hose, flex conduit, or bicycle tire. Drill some holes and use lacings or zip ties to attach the hose.
5. Attach the boss if there is one. Mark the center point of the shield, cut out a circle the size of the dome, and then bolt on the boss. Make sure the bolts are facing inside and don't extend more than 1/2 inch past the nuts. I recommend nylon lock nuts so they don't come loose.
You will also need to add a handle if your boss doesn't come with one. A pre-fab wooden tool handle from a hardware store can work well if you shave one side flat and bolt that side to the shield. Ideally you should leave the part this fits inside the boss un-shaved to move your hand further into the shield so it balances better.
6. If there's no boss, add a strap and a handle. Mark the center point of your shield by weight and place your forearm on that point, centered, at about a 30 degree angle, and trace the outline. Mount a wide strap (like an old belt) with a buckle vertically so it lines up about 2" past the bend of your arm, and attach the bottom of the strap about 3" below your arm.
For the handle, you can use a strap or a pre-fab handle from a hardware store, or build one from wood or metal. The important part is that it's sturdy and that you have enough room for some padding behind your hand.
When lining up your handle, place your arm in position against the shield and notice the natural grip angle of your hand. Your handle should match this angle.
You will also need something to cover your shield hand, which may be leather, metal, or plastic, as long as it is either supported to not collapse into your hand or has enough padding. Alternatively, you can buy a pre-made shield basket with an integrated handle, though these are often heavier than they need to be.