What underlay is used for installing pool tiles
You are going to use pool plaster to build up the area, modified thinset to apply the tiles and epoxy grout to grout the area.

Additional info - 

Your pool will generally have a pool plaster for the "liner" (what you feel).  It could however have a ton of products - example is pebbletech - for this.  It really depends on how nice your pool is.   Pool plaster is generally made of concrete, sand, and quartz.  There are other combos and there is premade combos too.  If you are doing your whole pool then you can choose whatever you want - each will have their own characteristics.  If you have a question on this I would ask it on its own since you will get a lot of different views/help.

If you are doing patchwork then you will need to try to match up the characteristics of current "lining".  This will take practice/guesswork and maybe bringing in a little experience.

For the tile section at the top of the pool you generally want to buy tile that curve towards the pool bottom so there is a smooth transition or you will need to feather up to the tile area with a thicker amount of plaster (they sell very expensive "pool tile" for this).  This will create an indention to apply your thinset and tile.  And you will basically tile as you would a shower.  

I would use a modified thinset that is best suited for the type of tile (a lot of pools use porcelain) you are using.  Note that under your tile should be sealed with pool plaster.  So the tile is really just decorative.  This is where there are differences in showers and pools.  Using tiles on the top ledge or steps in pools should be used to provide a nice surface/decorative - not as any sort of moisture barrier.

A lot of DIYers use "regular" porcelain/granite tile (I would not use marble or ceramic and I would make sure the porcelain I use has a low absorption rate) and can buy everything from a big box.  The hardest part is making sure the tile plus thinset depth is close to the depth of the adjoining plaster - for pool steps you don't have to worry about this.  

And if you are replacing tile a lot of the stuff should be kind of set up for you.  You will damage some of the plaster when chipping out the old thinset.  You might have to make some repairs - I guess if the repairs are behind tile your plaster type is less important as long as it bonds.  Also you will need to match up the old tile thickness to the new tile thickness.  If you go with a new "thicker" tile it could create a lot of work because you may only have so much plaster you can get rid of before you hit the concrete base.  In general almost all pools with a tile layer on the top sides have a "lip".  You won't match it up exactly.  But you want to make sure that it isn't dangerous - as far as people scraping themselves.  And with a larger lip there is more upward force that could be put on the tile - causing more needed repairs down the road.