On carpet: Use the hook/male side of Velcro tape, available at home supply stores. Use approximately six inch pieces and strategically place them in areas under the putting green that will not affect the roll of the golf ball when putting, but will hold onto the carpet. Move the location of the velcro if carpet begins to fray.
On hard surfaces: Use both halves of the velcro, stick to bottom of green and stick corresponding side to the floor. This allows you to unfasten and move or roll up your putting green.