-Create a new black solid and drop a Fractal Noise effect on it. Add a curves and increase the contrast a bit (anchor the center, and then move brights up and darks down). Put this solid above your text layer.
-Select your text layer and change the track matte to Luma Matte.
-To have the text dissolve in, animate the curves on the solid so that it goes from completely black to completely white (or halfway to white, depending on how grungy you want the text to look).
-If you want the text to dissolve away, animate the curves on the solid so they go back to black
Ah great, thanks Brendon! I've seen this transition a few times so I'll give this a go. If I wanted to create a more defined edge to the text transition (as I've seen it were the text kind of comes in through curly shapes rather than a 'dissolve' as such, if that makes sense), would I use something different than Fractal Noise - maybe make a different displacement?
Sure! I think fractal noise will give you the desired look, but you can always change the "fractal type" within the effect for different looks. Animating the "evolution" setting can also give a slightly different look by making the pattern "crawl" more.