This method can be used with ribbon, or fabric strips or you can use construction paper, comics, wrapping paper or other colorful paper for disposable placemats

Start by assembling the strips and cutting 1" longer than the finished length or width.

then take the up & down strips, and tack them to a cork board or other board to hold in place on one end. It is easier if you tack the end farthest from you, leaving a space between the strips to insure it does not warp as it is woven

Start weaving the across strips as you place a dab of glue between the ribbons where they cross
Use fabric glue for the ribbon or fabrics, white glue for paper strips

Allow to dry

Trim the edges to the desired length
Fabric or ribbon edges can be stabilized by carefully dabbing a bit of fabric glue on the ends to prevent fraying