Here's an exploded view of a grasshopper mouth (they're fairly close relatives):
On top is the labrum, which is like the top of a beak. (Ignore the face plate (clypeus) above it, it's not important.)
On the bottom is the labium, which is the bottom of the mouth.
To the sides are the maxillae, which are kind of like cheeks, if your cheeks could open like a sideways beak. (Singular is maxilla.)
Finally, there are the mandibles, which are like big incisors that flip out when it's time to eat or bite something. Most of the time, they're tucked away under the labrum and the maxillae.
(Bonus: The hypopharynx inside the labium is basically a tongue! It even has a salivary gland at the base.)
In addition to the antennae, roaches have four palps, which are like little antennae on the mouth for tasting food. There's one on each maxilla, and two on the labium--maxillary and labial palps, respectively.
Now, here's a render I did of Sophodra's mouthparts flared open (mantises are even closer relatives of roaches than grasshoppers are):
You can see that the labium is split into two halves, called the prementa. Additionally, each prementum has two little fingers at the end, the glossa (inner) and paraglossa (outer), for four little fingers in total.
The maxillae also have their own fingers at the ends, called the galea (on top) and the lacinia (bottom). Overall, these eight fingers act like lips, letting the insect manipulate food better.
Sadly, I don't have many good gifs of roach mouthparts working, so here's a look at them in motion on a mantis (the mandibles have black tips, the insides of the maxillae are red):
A better look at the mandibles:
A better look at the maxillae:
And now for the best gifs of roach mouthparts I have!
Sorry :( Hopefully that gives you a good enough idea!
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