In an effort to drop our monthly expenses and spend more time together as a family, we are cutting the cord from cable. We're keeping the internet... and I can't completely shed TV. I still want to see a radar, watch football, breaking news, etc. So I decided to build an HD antenna, which allows me to get all of the major networks plus another 15-20 channels (your mileage WILL vary based on your location and topography). This assumes that you have a relatively modern TV. If not, you'll also need a little box that will convert the digital signal to the air. You can pick a quality one up on Amazon for $20-$40 (search "digital converter"). You'll save that the first month you ditch cable.
A little background: Since 2009, broadcasts are provided in digital formats over the air. They are almost all in the UHF frequency range, with a few in the VHF range, and most of those in the nigh VHF (near UHF range). This means that a UHF-only antenna will typically get you what you need. To figure out what you need, go to
TV Fool. You can get stations in your area to help select/aim your antenna and see a coverage map to know how much meat you need in your antenna. In my market, there is only 1 station in the VHF range at channel 7, so it is high enough frequency that a UHF antenna will do. Further, I'm on a hill so have line of sight (for RF) out well past the 20-30 miles I need, so my antenna is up in the attic. Depending on your situation, you might be able to just put this right behind your TV. Here's what I built and what you'll need to do the same.

Material:
4 all-metal coat hangers (not with the cardboard bottom for pants)
2 pieces of wire/coat hanger/other conductor about 30" long to connect the elements
10 bolts/nuts (I used 2" #6x32)
10 finish washers (flat washers OK, but finish washers hold down elements better)
1 Mast (I made mine by taping together the 3 legs from an old easel, ANY non-conducting strip of material will do... plexi glass, PVC, even cardboard)
300:75-ohm matching transformer ($6 from Radio Shack, this is the thing that has 2 terminal connectors on one end and a coax connector on the other... think old TV antenna connection).
Tools:
Safety glasses
Wire cutters (that can handle a coat hanger)
2 Pliers (to bend coat hangers)
Ruler/Measuring Tape
Sandpaper (I used 320 grit, any coarse grade will do)
Sharpie marker
Drill
Electrical tape
OPTIONAL: Soldering Iron
Construction:
I. Make elements (Put on your safety glasses for this. Sometimes the coat hanger parts will fly away. You don't want them to end u pin your retina.)
1. Clip hangers at the "neck" to get rid of the hanger part.
2. Straighten each hanger using 2 pairs of pliers (or by hand if you're a machine).
3. Clip the hangers into two 16-inch lengths (you'll have an inch or 2 left over).
4. Sand the coating off the middle of the hanger. This is REAL easy and quick... 5-10 seconds per piece. You'll know when you've succeeded because the hanger will be bright silvery virgin metal.
5. Meaure to the midpoint of the elements and make a small mark.
6. Using the pliers, bend each piece of hanger into a "V" with a relatively tight corner. You should bend the V so that the tips are 5" apart, leaving each elements with 2 8" arms 34-degrees apart. Unless you are a machine, you won't be able to get them all exact. Don't sweat it... make one good one, compare all the other ones to that one.
7. I used some red duct tape I have to make a small tab on the end of each element. These things are sharp and could easily end up inside my skin or my eye. This is an EASY precaution. Use the electric tape here or anything else non-conductive that you'd like.
II. Make base
1. Starting a few inches from the top, mark 4 sets of 2 holes spaced every 8 inches down the length of your board. The distance is about an inch apart but not critical for this application. I used 450-ohm window line (I'm a radio nerd).
2. Also mark 2 holes at same distance apart between the 2nd and 3rd set of holes. You end up with a hole at 0", 8", 12", 16", 24" from your starting hole.
3. Drill the holes out large enough for your bolts to go through.
5. Insert the bolts with the washer on the top side and get the nut started on each one.
III. Assembly & Installation
1. Lay your long connecting wire down so that it will be connected to the top/bottom ends on one side of your board and the middle 2 connections on the opposite side of the board. Your conductors will cross at each end. You can see that in the photo above. If you aren't using an insulated wire to begin with, you should insulate the two from each other where they cross. If you need to do this, wrap one or both wires where they cross with electrical tap. It should be laid out like this:
1 2
x
2 1
| |
2 1
X
1 2
2. Install each element (opening of "V" facing out as shown in picture) under the washer, making sure that it makes good contact with (is "squished" into) the long connecting wire. Tighten it down well.
3. Even our the elements so it looks like you ahve 4 X-wing fighters stackd on top of each other.
4. At the middle bolts, slip each of the terminals of the 300:75-ohm matching transformer thingamabob under one side of your connecting wire and around the bolt. Tighten it down well.
5. If you used bare wire for your connecting wire, cover it up with electric tape where the end of the transformer ends up. You don't want to create a short circuit in your antenna by letting the metal coax touch the connecting wires. That'd really mess up the RF response to this thing.
6. OPTIONAL: I you'd like to really do this thing up, you can solder all of the metal-to-metal connections. As this is a receive-only antenna (no radiated power) that won't see any external stress (wind/rain), this step is beyond overkill. If you think this step is necessary, you are advanced enough that you didn't need this how-to in the first place.

7. Connect a length of coax to your TV and to your antenna. Put the antenna as high in your house as you can and away from metal ducting. My cable was already run through my attic. So I just disconnected the TV cable from a splitter and connected the antenna.
8. On the TV, navigate to the Channel area of your menu and the "autoprogram"
The TV will run through a scanning sequence to find all the available channels. Compare the results your TV ends up with to those from your "TV Fool" report (at the link above). If you didn't get everything you expected based on the reports, there are a few things you can do in the DIY world (amplifying it is probably a step too far):
a) Raise the antenna. Height above ground is your friend. The higher you go, the fewer leaves/trees/buildings the signal has to get through between the transmitter and you.
b) Build 2 versions of this antenna and connect them together. If you want/need to do this, here's a schematic. Note: Balun is another term for matching transformer. This also has a reflector to further boost/directionaliz your signal:

My boys fell asleep during construction, so they will be helping me when I upgrade mine to a two-bay antenna and hang that one with some 550lb paracord at the peak of my attic. I want to get everything I can an potentially use it with my handheld HAM radio too. So I'm looking for a little more gain.