No problem, 1968billsfan. Craft foam is a soft, flexible material, a synthetic foam sheet. It is available in different sizes, and colors, from most craft stores (Hobby Lobby, Michael's, Wal-Mart's crafting supply section, etc.). Here is a link to Michael's web site, for this exact item: link.
For the vinyl floor tile, the pattern of it does not matter, as that side will be down, when in use on the table; the foam will be the top side of the tray, with figures resting on top of it.
Buy the cheapest pattern of floor tiles your supplier has. Cut it with a utility scissors, to the desired size, then peel off the paper, exposing the glue side. Apply the foam (either side, as it is the same on both) to the tile's glue, press down firmly, to smooth it out, and adhere it fully. Then cut the foam to the tray's size, and paint the foam.
The edges of my trays, and those shown, above, by the original poster, are made by gluing another layer of foam to the foam tray surface (before painting). You can use PVA Glue to adhere the foam, if you like. There are also specialty foam glues available at craft stores, if you prefer.
The OP's tray shows a foam border. This is useful in keeping the figures from falling off the edges of the tray when moving it. I later chose to remove the border foam. I chose to keep my mini's bases flush to the edges of my trays. My game's rules dictate that bases must be in contact for melee to occur, so it was just simpler to leave the borders off, and cut the trays to the correct size for the figures resting atop the tray: for close order troop types, they must all be in base-to-base contact, with each rank also touching the rank in front. My trays will hold standard figure bases in neat formation, edge-to-edge, front-to-back. This makes them useful for any figure/troop types.
The photo's of my trays on my blog, show strips between ranks of red Goblin figures. I did this, in the original project, because the Goblins are open order troops only. They cannot stand base-to-base to fight, they are not trained for close-in fighting. I later discarded the dividers to make my movement trays more universal, so that I could use them for any troop type, not just Goblins.
Let me know if I failed to explain my techniques properly. Thank you. Cheers!