Replacement ceramic tiles can be hung with straps attached to the back of the tile. Do not use exposed strap hangers because they make the roof look bad and they fail prematurely. The copper strap shown below can be altered to fit almost any type of ceramic tile, including Spanish tiles. It's a good idea to put caulk/adhesive between the copper strap and the tile to help adhere it into place. Use copper wire to tie the strap to the hanger. 14 gauge single strand insulated wire works well.
The illustration below shows the back side of the tiles and how the tile hook holds the tile in place. Tiles are usually loose enough on the roof that you can slide the tile and hanger in place without any problem. The replacement tile hooks on the existing tiles. When the job is done, there is nothing visible on the surface of the roof that shows a repair was made.
Valley (and general flashing) replacement on a tile roof (see below) is similar to valley replacement on a slate roof. The tiles must be removed to expose the original flashing metal, the metal must be fully removed, and then the new metal must be installed. The tiles are refastened into their original positions. Tile hangers (as above) are used where the tiles cannot be nailed, and copper wires are used to hang the small triangular pieces into the valley since you do not want to nail through the valley metal except along the edges. Note that each tile is numbered by scratching with a nail before removal. This makes replacement of the tiles a quick and accurate job.
73 year old Ludowici Imperial tile (a flat shingle tile) at Grove City College, Grove City, PA . We're replacing all the original copper valleys with 26 gauge terne coated stainless steel (above). We also rebuilt the plumbing vent pipe flashings using 4 lb. sheet lead, and reflashed the chimneys with terne coated stainless steel (below).