MIDI over ADB
TouchDAW 1.3.5 added support for running MIDI over the "Android Debug Bridge", aka ADB. This provides a fairly solid USB based connection that does not face the limitations coming with the tethering approach. In particular it works nicely across operating systems and does not require the Android device to be equipped with cellular connectivity.
Note: This is a hack providing much asked for wired Usb functionality that Android had no direct support for before Marshmallow. It may not be as convenient as one has come to expect from desktop operating systems' USB support!
Get required software
Discover and connect
Troubleshooting MIDI over ADB
If your device is not found, try changing the USB mode (from Media Device to Camera or vice versa). On some devices adb seems to work in only one mode.
Still having problems finding the device? Before you put the blame on TouchDAW or mnet, type the phone model and "adb" into Google. You will very likely find plenty of posts from developers struggling to get their device seen by adb. Go through the replies, somebody will have solved the problem. This is Android, you can not take anything for granted. Some vendors may supply extra development drivers, some devices may require Google's universal USB driver.
Sync software interference
There is a chance that sync software provided by device vendors (like HTC Sync) may interfere with mnet's access to the phone or tablet. In case the device is not found or you get error notifications saying the connection was refused, consider removing that software or temporarily disable its adb access.
Trouble after Android system updates:
After system updates an Android device will usually have a different ID, which will make the scanned address that mnet refers to invalid. Unpatch all present ADB channels, shut down the driver, relaunch it and rescan ADB. It should then find the device back again.
In some cases system updates seem to completely disable adb functionality on the driver level under Windows (seen for example with Acer's ICS updates). The following procedure should make it functional again:
Android 4.2.2 introduced a new security barrier to prevent unauthorized adb access. mnet uses an adb version that should handle this without problem, but you may need to add your computer(s) to a list of trusted hosts. Android should present a confirmation dialog when making an adb connection. Find further info in this detailed blogpost by Nikolay Elenkov (Google's official release notes are rather vague about the topic).
In case you get an "offline" notice on older Android versions, here is a Stack Overflow thread presenting possible solutions. The adb version mnet uses is in Program Files (x86)/humatic/MIDIHub/mnet/lib. Run terminals from within that directory.
Mac OS X:
If no devices seem to be found, you may have EasyTether or some other tethering solution installed or happen to have hit a OS / Android SDK version conflict. Visit this page on stackoverflow to learn how to solve that.