I'm Rob, one of the co-founders of Crittercism. Yes, it really is that straightfoward as adding the jar and initializing the SDK with:
Crittercism.init(getApplicationContext(), "CRITTERCISM_APP_ID");
An easy way to check that you've integrated correctly is by loading the live stats page in your app (there should be a tab on the left hand side of the page labelled "Live Stats"). On that page, you can see a live view of the app sessions, crashes, and handled exceptions in real time. You can load your app in a simulator or on an Android device and watch the app loads graph go up and if does, then you should be good to go.
Also, as @EddieFreeman mentioned above, you can intentionally throw an exception somewhere in your app (most developers tie this to a button click) to simulate a crash. Just make sure you take it out of your app before submitting to the app store :)