It depends at what level you are doing changes. If you are doing frameworks/base/core changes then you can navigate to your frameworks/base/core portion of your AOSP project and do an incremental build by doing (ensure that you initialized your build environment: . build/envsetup.sh in the root of your AOSP source directory):
mm -B
This will build the component you are in, which will be framework's framework.jar/ext.jar/etc
After this compiles then you can do (Be on the lookout for Errors during compilation):
adb root;
adb remount;
adb sync;
adb shell stop;
adb shell start
This will update the framework jar file on the device and then you should be able to see your changes.
Note
This will ONLY work if your current build is the SAME as the AOSP code you are building, otherwise you will have to push the framework.jar file into the system/framework/ portion of your device (which requires root).