There are numerous different ways to mount a TV antenna on a house or other building. The choice of method will usually depend on the style of roof. A usual good rule is to mount as a high as practical to ensure the best possible signal.
I’ve also written an article on how not to mount a TV antenna called Bad TV Antenna Mounts.
Tripod Mount

The most common current method of mounting antennas is the Tripod mount. These consist of a small metal bracket with two short supports, a ring and short pole(usually 1.2m). They come in two varieties:
Both types use two screws that fasten the bracket to the the roof batten. The pole goes through the ring and is bolted to the base. The pole angle can then be adjusted so the pole is vertical.
Advantages:
- Simple installation
- Can be mounted at any suitable location on the roof
- Stability

Disadvantages:
- Incorrect installation may result in roof leaks
- TV Antenna cable must penetrate roof
- Limited pole height(usually not an issue in good signal areas)
See the full articles How to Install a Tile Roof Tripod and How to Install a Metal Roof Tripod.
Fascia Mount(also known as a Hockey Stick or J-Pole)
A fascia mount pole is attached to the fascia board of the house just underneath the guttering. They are usually only suitable for wooden fascias because they attach using coach screws, but sometimes they are with metal fascias provided there is a block of wood behind the fascia to screw in to. They are typically available in sizes of between 1 and 2 metres. With taller poles they may need to be stayed.

Advantages:
- No holes in the roof for screws, so less risk of leaks
- No roof penetration required for TV antenna cable
- Simple installation
Disadvantages:
- May not always stand perfectly vertical
- Strong winds dragging on antenna may warp fascia board over time
- Because they are based at the bottom of the roof the antenna is usually quite low
Pole and Metal Stays
In locations with weak Digital TV signals it may be necessary to use a larger antenna with higher wind loads or a high pole to get better signal. One method is using a light angle roof mount, longer metal pole and two metal stays. Typically these style of mounts will go to heights of 1.8-3m, which is often enough to get good signal in weak signal areas.

Advantages:
- Able to reach higher than tripod and fascia mounts
- Very stable
Disadvantages:
- Twice as many screws required to attach to roof, so can risk leaks
- Much more elaborate and ugly
Telescopic Mast
Telescopic masts are used in the worst TV signal areas. They can extend anywhere from 7-15 metres. Specialist installation is required as there is a risk of significant damage if the mast falls down. They usually require 3 or 4 sets of guy wires to hold them in place and are very difficult and time consuming installations.
Advantages:
- Height enables better signal in bad reception areas

Disadvantages:
- Very ugly
- Must be carefully installed to avoid risk of the mast falling and doing significant damage to your property.
- Difficult and time consuming installation usually requiring at least two people.
- Repairs or maintenance is difficult because mast must be lowered and extended again