The fuel sender, for the typical US standard used in a marine application, is a simple device that presents a resistance reading to the gauge with which it is paired. For US fuel gauges, from the likes of Stewart Warner, Faria, Vee-Three, Moeller, Teleflex, Tempo, Westerbeke, Universal etc. this reading is 33Ω - 240Ω.
In order to test your sending unit simply connect a DVM turned to the Ω setting to the center stud and ground reference. On this particular sending unit, from Moeller, ground reference is the flange or the male Fast On terminal I am connected to.
In this image the tank float arm is vertical or reading empty and we can see a near perfect 237Ω reading. This sender is reading empty just about perfectly.
There are three basic types of fuel sender readily avaible at most marine chandlers.
#1 El Cheapo Type - The one in this photo is the style I refer to as the "El Cheapo".. They are inexpensive and last about as long as the flavor of the gum in a pack of baseball cards. I replace this style sender about 10:1 over the other types mentioned below.. If you have one like this, and it has failed, look into the other types shown in this article.
#2 WEMA Type The WEMA sender uses a float that rides up and down a sealed dip tube. No electrical components are inside the tank and exposed to fuel. They are very, very reliable. These senders are sold by WEMA, the actual manufacturer, and re-labeled by companies such as Moeller and others.
#3 Mechanical Sender With Electric Conversion Capsule This is one of my personal favorites, It is what I choose on my own vessel. The float is attached to a gear drive which turns a magnet in the head/flange of the unit. There is essentially nothing to fail in these senders and I have yet to see one that has. They are sold first as an unbelievably reliable mechanical sender with visual gauge but with the addition of a "conversion capsule" you have both a mechanical gauge and electric. If the electric gauge should fail you can still read the level of the fuel by looking at the mechanical gauge.