Remove the casters from your chair. These are normally anchored to the bottom of a chair by way of turned bolts. You will need to use your Allen wrench. There should be four main screws.
Check to see if your chair has a solid wood base. This is common among furniture made prior to the 1980s. You can check by knocking on the baseboard. If the knock sounds more "deep," you have press-board. If it sounds higher, then you have solid wood.
Affix the leg anchors to the four corners of the bottom of the chair by way of 1/4-inch wood screws.
Screw the chair legs to their anchors if required. Some chair legs come attached permanently to their anchors.