HL2SAV
The NOAA APT weather satellites broadcast their signal at about 137 MHz, and their signals are also right hand circularly polarized (RHCP), which means you will need a right hand circularly polarized antenna to properly receive the signals. This is because as the satellites broadcast their signal, they also rotate, rotating the signal polarization. Satellite antennas are also designed to receive best from signals coming from the sky. Three options for easy home made circularly polarized satellite antennas are presented below.
A turnstile antenna is a circularly polarized antenna. It can be built in two modes, normal and axial. For satellite reception we want it in axial mode.
A page showing a turnstile antenna for 137 MHz is here.
A Quadrifilar Helix (QFH) is a circularly polarized antenna that can be constructed out of PVC pipe and coax cable. Most people report that the QFH antenna has slightly superior reception compared to the turnstile.
If you are into antenna theory, a good technical paper on the QFH (called QHA in the paper) can be found here.
A tutorial on building a QFH out of coax cable and PVC pipe can be found here. Another home brew QFH antenna constructed out of copper wire is here. Also, a good calculator for determining QFH antenna dimensions for 137 MHz can befound here.
Another antenna that works well with the NOAA APT satellites is the double cross antenna (DCA). It is basically four dipoles arranged in a certain way to produce circular polarization.
A good guide on DCA antennas, and constructing them can be found in this pdf guide by Gerald Martes (KD6JDJ).
Yagi antennas can also work, but since they are so directional you will need to carefully track the satellite by hand, or by using a rotor controller. Although not designed for satellite reception, you may also see limited success with other antennas such as quarter wave ground planes and discones, but you will probably discover that the signal will fade in and out.