Photometry Light Curves
The goal of photometry is to produce a graph that shows the changing light emitted by a star. One example is the graph below. Its the light curve for the Eclipsing Variable Star U Cephei.
The Star's magnitude is plotted along the y-axis. Since higher magnitudes correspond to dimmer stars its graphed in reverse order. Time (in Julian Date) is on the x-axis. Julian Date (JD) is often used because it provides a simple way to record time as rational numbers with having to worry about fractions of hours or daylight savings time or other interesting quirks of a 24 hours clock.
In principle doing differential photometry is very easy. All you need is a tripod and a DSLR camera that can take long exposure photographs. If you uses a camera tripod that isn't capable of polar tracking the exposure times will be limited to about 30 seconds (depending of the lens you use) before the stars will begin to trail. I attached my DSLR camera to my 85 mm refractor and used my tracking mount; in this configuration the exposure time is limited by the saturation limit of the camera. Depending on the target that can be anywhere from a few tens of seconds to a few minutes.
Choosing a Target
There are thousands of variable stars within reach of surprisingly modest equipment. A simple tracking mount and a DSLR camera can record variations in stars as faint as 11th or 12th magnitude. An 11" telescope can reach as far as 14th or 15th magnitude.American Association of Variable Star Observers. You'll also find a huge amount of reference and resource information on the how-to of pretty much every aspect.
Aside from the magnitude of the variable star you chose there are a few other things you should consider. How big will the variation be and will your equipment be sufficiently precise to measure it accurately? How often will minimums occur and will they occur when viewing is favourable? How high in the sky will the target star be? For people who have done astrophotography most of this is routine but if you're just getting started its important to keep them in mind.
There are several different software packages that are capable of taking raw camera data and producing useable photometric data. The three that I recommed are:
AIP4WIN is another great alternative. It costs about $100 but comes with an excellent book (or the book comes with AIP4WIN, depending how you look at it) on variable star observing. Aside from a quick cursory look at it I haven't used it but I heard excellent things about it.
If you want a sleek, well thought out, multiuse software package (and don't mind spending $600) then check out MaximDL. It will do pretty much everything an astronomer or astrophotographer could ask for, including Photometry. Beware: The basic and DSLR versions DO NOT come with photometry tools!
Below is the (partial) light curve for W Ursae Majoris. This is a contact binary system with a period of just over 8 hours.
The x-axis is typically in Julian Date since you don't have to worry about the 24 h clock and things like daylight savings time. To convert from our normal 24 hour clock/date to Julian Date I've used the USNO Julian Date Converter. The results you get from DSLR or CCD cameras are ADU (analog-digit units); basically a measure of how many photo electrons are recorded in the sensors. These are basically telling you what the intensity of the star is. However to create a light curve like the one above you need to change intensity to magnitude. You can do that using the equation below:
m1 - m2 = -2.5 log(I2/I1)
This equation will basically tell you the difference in magnitudes between two stars. So that means you actually have to do a measurement on TWO stars. One that has a constant magnitude and your variable star. Then you plug the intensity values into this equation and you get the difference in magnitude. In fact, spreadsheet programs like Excel can actually automate most of the calculations. The result will be a nice light curve! And just think about what this curve shows! You're looking at subtle changes in stars light years away!