Good question.
It depends on the lake and it's an educated guess to a certain extent. First thing obviously is chuck a lead out there, see what kind of drop you get and how badly it's plugging. If it's a generally silty lake I might then have a lead about in the margins to compare, I normally find the silt in the edge is a little deeper than in the middle. A landing net handle can help here too.
If it's just a silty spot in a relatively none silty lake the drop will normally tell you all you need to know.
I used to play about with white string tied up the leader - cast out and the silt discolours the string giving you a good idea of the silt depth - I no longer do that however as it's a bit of a faff and tbh I don't think you need to be that accurate unless you're using stiff rigs (I moved to 15 lb from 25 lb fluoro for this reason).
Tbh nowadays I'll normally just have a chuck about with the lead, I've been doing this a while so can get a pretty good idea doing just that.
On the odd occasion when you find silt that's literally feet deep, you can limit plugging to say 10 inches or so by feathering the cast.