I run Legacy and DCS and use my iPad to control turnouts using the LCS system. You can do it for a lot less money with ASC ($35-$45) rather than ASC2 ($90-$100) modules. You will need 8 ASC devices (each will control 4 turnouts), LCS WIFI ($130) module, one LCS DB9 cable and power supply ($27), a Cab1L command BASE ($105) or a Legacy Command base, a SER2 module ($36), the free LCS app.
The advantage of using ASC rather than ACS2 modules are that they are half the cost and can be connected together with plain wiring, rather than the expensive LCS cables ($14 each). They can control either momentary solenoid turnouts or stall motor turnouts (eg, Tortoise). ASCs are out of production, but I had no trouble finding them at train shows, on the forum and on the bid auction site.
The STM2 devices mentioned by George are optional. They add a feedback on turnout position, but I have not had any problems with my iPad being out of sync with the actual turnouts. So, I have not used them.
If you have crossovers, you can get by with even less ASC modules by connecting both turnouts to one set of relay contacts. You tap on the crossover on the iPad and both turnouts throw. If you have 4 crossovers, you can eliminate 1 ASC module.
Here is a diagram of the LCS setup that George described. Mine is similar except there are no ASC2 modules, but instead, all the ASC modules are daisy chained off the SER2 module using plain wire.
If you decide to go with ASCs, I can draw a wiring diagram for you. It's a little more complicated than the plug-and-play LCS modules and cables, but it's not rocket science either.
Here is the yard portion of my track plan with multiple crossovers. Main route shows in green and alternate route in red. Tapping a turnout throws the turnout and reverses the colors. A second tap toggles it back.
Go Here for a thread with more discussion of iPad turnout control.