I have seen a wide variety of methods being used. For smaller machine (Shapeko, Zen robotics, etc,.) I have seen people using double side tape.
Many people will screw down their pieces to the spoilboard. Most consider the spoilboard to be sacrificial and regularly cut into it, and then periodically resurface it.
I differ from most. I treat the spoilboard like the top of my workbench. It needs to be a flat reference to enable accurate work. Just like I do not purposely screw or cut into my workbench, I do not cut or screw into my spoilboard. Like my workbench, I have clamping provisions on my cnc (dog holes and t-tracks). Like my workbench, it is not a piece of furniture, and an occasional ding or two is no cause for concern, just make sure they are scraped to be below flush.
There are two main types of cuts using the cnc router. First is carving or engraving - there have been many posts here of signs or carvings. For the carvings to be uniform, the spoilboard needs to be flat, and parallel to the X Y plane of the cnc (I.e. Constant Z). That is why you will see people "surfacing" the spoilboard or milling it to ensure it is flat and at a constant Z (and also complaining about the huge amount of mdf dust this process generates). I chose to surface the under structure and attach a uniform sheet to the top of that. Less dust.
The second use of the cnc is to cut out parts (in software these are usually called "profile" or "contour" cuts). In these cuts the bit goes all the way through the workpiece. This is the type of cut that will chew up the top of the spoilboard and require periodic surfacing. To avoid this I simply add sacrificial spacers made from 1/8 hardboard under my hold down clamps. I can then safely cut through the stock by .03-.05 and never damage my spoilboard.
Many operations of course have both carving and profile cuts in the same piece, and are usually done in a single setup with only bit changes.
For either of these type of cuts, to secure the workpiece to the CNC you need to keep it from moving, and you keep it down flat against your reference. The common hold down clamps that engage into T-tracks do the hold down, but may still allow the stock to slide. On my CNC I have a series of dog holes along one end and one side. I use cheap plastic dogs in these holes (mine are from Rockler, but dowels and wood blocks would work as well). I then wedge the stock against these dogs to keep it from moving. I then have several have several clamps that hold the work down using T-slots machined into my spoilboard.
The cad/cam software (Vcarve, Aspire, ArtCAM or Fusion 360) you will use all have provisions for adding "tabs" to keep any cutouts in place - this serves the same goal of keeping the piece from moving and held down. Once the piece if done with cnc operations, you remove it from the cnc and either snap out the part, or cut it out with a knife or small saw, then sand or use a flush trim bit in router to remove the tabs.
My recommendation is to manually place the tabs where they are easy to trim, and not be stingy with them. As the profile cuts are usually done last, you don't want a workpiece to be damaged by prematurely breaking free!