As usual, there is no definite single answer to this question I believe. It depends in what you are interested in. One way to trace the degradation of a gel is to constantly monitor it by rheology while it degrades. This will give information on the time-dependent alteration of the gel mechanical properties, which can be translated into other information, for example, into the polymer crosslinking density by use of the phantom network model based on the theory of rubber elasticity (G' = v RT, with G' the (in your case time-dependent) elastic shear modulus and v the (corresponding time-dependent) crosslinking density, assuming tetrafunctional polymer-network junction nodes). This approach will tell you how the elastic modulus or the crosslinking density derived thereof decreases as a function of time. Another elegant way is the one suggested in the preceding answer by Stefan Röhner, which focuses on tracing the molecular weight. A third very simple way is to simply visually monitor the gel degradation. My group hase done so in a recent work using a microfluidic platform...see Macromol. Rapid Commun. 2013, 34, 1401-1407.
There are many methods that can be imagined to work similarly. Basically, they all share the same principle: chose a property that you are interested in and that changes during the gel-degradation, and then trace it as a function of time.