There are many ways to adapt contractor-style table saws to dust collection systems. They all tend to follow a common blueprint, but naturally they range from simple to complex, depending on how much effort you want to put in and how much dust you are willing to let leak out.
Image credit: WOOD Magazine
The solution above, Tip #9 from this collection of tips at WOOD Magazine, is among the simpler systems, which makes it a good illustration of the basic technique. You place plywood between the base and the saw so dust doesn't fall out the bottom, attach a port for a dust collector or shop vac, and cover the back so the sawdust is captured. This particular version has some downsides: first, the blade can't be tilted while the back panel is on. Second, the airflow path isn't shaped -- it mostly enters from the opening in the back for the motor and exits straight down the pipe, which means dust will still tend to collect in the corners.
Stepping up a bit in complexity, you can somewhat solve the problem with the back panel by having different back panels for common angles. You could have one for 90° and one for 45°, each shaped to cover the gap with the saw tilted at that angle. The back panel can be attached various ways. Here are examples using magnets or with Velcro. Pictured below is an example of that technique, with the blade titled at 45° and the corresponding panel installed.
Image credit: American Woodwoker Editors / Popular Woodworking
In that picture you can also see an example of a more complicated technique to prevent dust from building up. Instead of using a simple plywood base across the bottom, they use the space under the stand to build a sloping profile so dust will tend to fall towards the relocated collection port.
And there are even fancier options. I particularly like this system from Richard Babbitt published in Fine Woodworking, first because it takes airflow path into consideration, and second because it completely encloses the motor, allowing full use of the table saw's tilt function without compromising the dust collection system. The box enclosing the motor doubles as a short outfeed table.
Image credit: Fine Woodworking
To quote the Richard Babbitt, "No matter which type of saw you have, the principle is the same: Close off most of the saw, allow rapid airflow in a few key areas, and you'll send the dust toward the hose and not into the shop." The pictured system has an additional benefit of drawing the air in across the motor, keeping the motor cooler in the process.
As you can imagine, the construction details of how this is accomplished are necessarily specific to each table saw. If you're inclined to go this route, I highly recommend Babbitt's article Dust-Proof Any Tablesaw in issue #205-May/June 2009 of Fine Woodworking. The full article is available as a PDF to digital subscribers of Fine Woodworking. It discusses design considerations, and how to adapt the concept to saws other than the ones pictured. It also has a section on improving dust collection for cabinet saws.