You have to beat the game in order to evolve your starter Pokemon. By finishing the main storyline, you would have to go on this mission featuring Manaphy. Check this (the top-voted answer) and this for detailed information. After you complete that, you can unlock Marine Resort Dungeon and you would be able to evolve at Luminous Springs. When you get there, you'll get a list of Pokemon that can evolve. Select the Pokemon you want to evolve and, remember, you can evolve multiple Pokemon at once. Also, be sure that you've done the little bits of the storyline that come after the credits. Here is a quote from Serebii about it:
When you first get the evolution option open, you will get notifications that your starter and partner cannot evolve. This is true to an extent, however when you have completely finished the storyline of the game (even the bits after the credits) with the icons as seen below, and have recruited Palkia, you will be able to evolve your character and your partner, so do not fret if you cannot seem to evolve it
If you check the second link I gave you, you can see at the bottom of the page the icons.
Skitty can evolves differently by giving it a Moon Stone, which can be found in the shops. For Torchic, it has to be the appropriate level and follow the steps I mentioned before.
I hope this helped!
Source: Links Above
