Normally, you would just be able to walk up to them and start a conversation by hitting their speech bubble. But...
Not being able to talk to NPCs in the mobile version is a known bug.
You may be able to force it to work by restarting the game, as this doesn't occur all the time for all players.
List of known bugs in the mobile version: http://terraria.wikia.com/wiki/Known_Bugs_(Mobile)
"The Mobile Version has a bug where in since 1.1.9, the player is unable to talk to NPCs."