This question has been asked before at How does Android enforce permissions?. While the discussions there are good, the question is still not fully answered.
In the development environment, exceptions are thrown when the app tries to do something that requires permissions not declared in AndroidManifest.xml. So how does the run-time system implement the run-time checking?
I guess it's most likely done in the core framework, which may or may not need support from native code. But I don't know what source code files in AOSP are relevant to this.
Android uses a lot of the standard Linux(-kernel?) mechanisms especially when it comes to hardware restrictions.
Every app gets assigned a new unique (Linux-)user id and whenever the app process is created the system creates it with that user id. The id will never change unless you remove the app. That means for accessing the lower system levels your app will appear as a certain user and every (Linux-)permission system that works with users will also apply to your app.
If you request
WRITE_EXTERNAL_STORAGE
in the manifest your app will also become member of the (Linux-)group (calledsdcard_rw
) that has permissions to write to that storage. Permissions on the filesystem are enforced to only allow writing to thesystem
user (=owner) and thesdcard_rw
group, anyone else (=other) may only read. See also Is Google blocking apps writing to SD cardsBy doing that Android has to do pretty much nothing except for setting the correct UID/GIDs of the processes it spawns once the app starts and the rest is handled at lower levels. Apps that are not member of a certain group simply don't get access to certain hardware.
List of permission <> group mappings: platform.xml
There are also some (Android software) restrictions that are based on either the signature of your app and / or simply by looking up the permissions your app requested: e.g. ContextImpl#checkPermission() - but those permissions have to be checked at every entrypoint to code that allows restricted actions.
From time to time people discover ways to e.g. turn on GPS programmatically because a check like that is missing somewhere.
With regard to your second paragraph, "exceptions" are runtime faults. Permissions are not enforced at build time, only at run time.
Accessing hardware, low level operating system resources, and system files generally requires the app userid to be a member of an appropriate group which it may be assigned by the package manager as a result of having a corresponding android permission. (Familiar examples of that would be network sockets, and the sdcard write which zapl mentioned, but also system-only things like talking directly to the GSM modem or reading the raw touchscreen coordinates).
For the majority of android operations that are done by way of calling library functions which are stubs for interprocess communication to services running in a different process, the platform code running in the more privileged process on the receiving end of the ipc request checks with the package manager to find out if the calling application has the necessary android permission.
Many special permissions are only available to apps signed with the system signature - even if another app claims those in its manifest, they will not be applied by the package manager.