I've found an ESD mat that comes with a grounding cable with an eyelet that's supposed to be screwed into the center (grounded) screw of an electrical outlet. But in my home, the outlets do not have one center screw; they have two screws, a top one and a bottom one. Would either of these screws be grounded? If not, how would I connect the grounding cable?
The round "D?" outlets use 1 centre screw. The square outlets use 2 screws for the cover.
Both are grounded.
You can file a 1mm slot for the wire exit and fasten to the metal box outlet then cover or use an external centre wire with a ringlug that is a threadtight fit. Your choice.
You can buy or make these and somewhere there is a 1Mohm R in series.
Removing the cover should reveal the bare copper ground wire fastened to the box. Just fasten any suitable wire to the box, file a relief slot for the wire to exit on the edge of the drywall and cover then connect to matt and use strain relief.
We are all making assumptions about outlet grounding, and that is not a good path to follow. Many homes over 70 years old may not have grounded outlets, so if you move into an old home as a fixer-upper, you may have to upgrade electric and plumbing to meet codes. One of my brothers moved into a old house 20 years ago and bought it twice after upgrading many things.
Though the electrical outlets had a grounding hole, the Romex cable was only 2 wire with no ground. So the refrigerator could shock you sometimes. The key is to remove the plastic plate and check for a bare 14 to 12 gauge ground wire. If it is there it will be wired to the ground lug on the power outlet.
Since it screws into what is sometimes a metal outlet box it is also grounded. But old bakelite boxes and todays plastic boxes are common, as code only requires that a ground wire of equal size to the power wires be run to each outlet. If there is no ground wire in the box it cannot offer you a grounded connection, and you must contact a certified electrician to run ground wires.
If there is a ground wire then the metal screws that hold in the plate should be grounded as well. The screws are normally 6-32 in the USA so a number 6 ring terminal with a wire crimp will get you a valid Earth ground.
It is understood that grounding codes in other countries may exceed or fall way short of USA NEC codes. Even more reason to take off a cover plate at least one time to verify the house / trailer / apartment has a ground wire. If wires are stranded the ground wire is often colored green or green with a yellow stripe.
Every Decora-style duplex receptacle that I have seen for the past several decades has two screws that attach the cover plate to the receptacle. Those two screws go into the metal frame that the receptacle is built around.
So long as the receptacle is properly grounded, either of those two screws are an adequate ground attach point for your ESD mat.
A great method of attaching to one of those screws is to use a #6 ring-tongue crimp terminal under the screw head.