Assuming you have MusiKloud (it's a SoundCloud client, of course!) installed, just starting the application will check for updates, as shown below:
The installer is saved to the root of your mass memory. You'll need to manually uninstall the previous version and then tap on the new installer to install as usual:
This manual removal of the previous version is because the application UID has changed in going from the Store version to the self-signed OTA version. Hopefully future updates to MusiKloud and other similar Symbian applications can be 'over the top' of existing installations.
In addition to the hassle of having to remove the original Store version, the developer also notes:
As it is no longer possible to sign Symbian SIS packages, the application UID has changed for MusiKloud 1.5.2. Unfortunately, this means that you will lose the archive database, as this is stored in the application private folder (generally C:/Private/$UID, or in the case of MusiKloud C:/Private/0x20068c6a). The only way to prevent this is to gain read/write access to these private folders and copy the database file from C:/Private/0x20068c6a to the private folder of MusiKloud 1.5.2 (C:/Private/0xe561675f). This may only be possible with custom firmware.
Ah well. Blame Nokia for freezing its Store in the first place?
Here's MusiKloud 1.5.2 in action:
In case you didn't have MusiKloud in the first place, you can buy it here in the Nokia Store and then update from there.