I have an older home (1969) & both the kitchen & bathroom sinks drain through the floor not the wall. I am looking for a diagram to show me the correct way the are to be installed. I have replaced them both before but I'm not 100% sure I did it correctly since they both seem to clog easily.

The only thing wrong with the drain going through the floor is that it means you have "S" traps. The only thing wrong with "S" traps is that they can be siphoned dry. Please note that I said can be, not will be, siphoned dry. It all has to do with the distance between the trap and the vent pipe and the size of the pipe. The greater the diameter of the pipe the further the vent can be from the trap. In order for the trap to be siphoned dry the drain pipe must also be fill completely with water. If you have a lavatory drain which has a 1 1/4" drain going into a 2" pipe you will never fill the 2" drain pipe completely with water. There will always be space at the top of the drain pipe for air from the vent so you will never siphon the trap dry.

You can see that figuring out whether a trap will be siphoned dry is not simple. Plumbing codes were change to require venting within a certain distance that would insure that a trap would not siphon dry regardless of the physical conditions. That meant that a drain line going through the floor and its "S" trap no longer met code because it could not be connected to the vent with in the required distance.

It does not mean that a "S" trap will not work if all the right conditions are met.

In other words "If it ain't broke, don't fix it".

If your traps are not being siphoned dry and you aren't getting sewer gasses I recommend leaving them alone. The only other disadvantage of the drain going through the floor and its associated working "S" trap is, it makes replacing cabinets difficult.