Disassemble your double bed. Set the mattress and box spring aside for another use or donate them. Determine whether the side rails hook into slots on the headboard and footboard or bolt on. Keep the side rails if you think that you might want to use your bed as a double again. Otherwise, discard or donate them.
Locate and buy a converter kit. These kits can often be found at mattress or bedding specialty shops. Whether your double bed takes rails with hooks or uses bolts, make sure the kit you buy has rails that attach the same way.
Install the converter's kit rails onto your headboard and footboard. If your headboard and footboard have slots, carefully slide the rail hooks into the slots until they feel sturdy. If your kit has rails with nuts and bolts, bolt the rails and the headboard and footboard together securely, without over-tightening.
Attach the two halves of the middle support bar. These two pieces swing out from the side rails to meet in the middle and help support the mattress and box spring. Secure the support bar as instructed by the converter kit's manufacturer--most likely with an included clamp. Twist and adjust the support bar's foot so it falls about 1/4 inch above your floor.
Attach the side brackets. The side brackets attach to the side rails to help hold the queen-size mattress in place and keep it from shifting. Of the four brackets included, two attach to each side rail. Most likely they bolt onto the rails using predrilled holes, but follow the instructions for your specific converter kit.
Place the queen box spring onto the rails and the queen mattress on top of the box spring. The mattress and box spring will hang over the rails by a few inches on each side, but the side brackets will hold them in place. Tighten the side brackets so they grip the box spring securely. Lock them in place using the hardware provided with the converter kit.