MarkG13 You don't need to do anything else! If you return to the "Home" screen now, you'll see the training progress. The selected Pokémon will slowly gain EXP (experience points) while your phone is face-down.
When your Pokémon gains enough EXP, its level ("Lv.") goes up. If you return to the "Home" screen again later, you may find that the Pokémon evolved to its next stage, which unlocks another entry in the Pokédex.
The level at which a Pokémon evolves varies by species. Not all species evolve, but the Weedle you picked will. Twice, in fact, as it's one of the Pokémon with two evolution stages. And being a Bug-type Pokémon, it evolves very early.
(Aside from evolution, certain Pokémon species in Glyph Catch only unlock after a certain amount of training, or after raising at least 6 different Pokémon to Lv. 70.)
