Grasp the edge of the curled linoleum and lift it upward until you meet resistance, or until the entire tile detaches. If the linoleum is too rigid to lift without bending, plug in a hair dryer and set it to high heat. Direct the air flow at the curled edge for 60 seconds to soften it.
Scrape the subfloor using a putty knife to remove all of the dried glue still attached to the floor. If any dry glue remains on the back of the linoleum, scrape it off as well.
Hold the linoleum up while vacuuming the floor underneath it to remove all dirt and dried adhesive particles. Vacuum very thoroughly, since any remaining material may interfere with the new adhesive or create bumps after reattaching the linoleum.
Open a small tub of linoleum floor adhesive and scoop out 1/8 to 1/4 cup, depending on the size of the repair. Use a putty knife for small curled sections and a notched trowel for larger areas.
Spread the adhesive over the subfloor in a thin layer as evenly as possible. Work the trowel or putty knife all the way to the edges of the bare floor area so adhesive covers it entirely.
Press the linoleum back down on the floor using your hands until it is flat. Roll the linoleum surface with a floor seam roller working your way toward a wall to smooth out the flooring and remove air bubbles.
Wipe the edges of the repair using a damp cloth to remove excess floor adhesive. Then place a heavy object on top of the repair to hold it down until the glue sets firmly.