[Transformer TF300T General] wha2do:
I wrote this awhile back to provide known methods to enter each of these modes. I know it's rather wordy, but may help those that are newer to all this. See the link below for a more concise write-up. I'll try to keep this updated with any corrections and/or new methods and feedback is very welcome.

How To Enter APX, Fastboot Mode and Recovery menu​

Special thanks goes out to tobdaryl for providing the foundation for this guide and to daws for

providing a previously unknown method (USB cable plug in while tablet is turned off).​

Pertinent links:

The methods below written more concisely by tobdaryl: How to enter APX mode or Bootloader-recovery menu

Universal Naked Drivers (for APX/ADB/Fastboot modes): [ADB/FB/APX Driver] Universal Naked Driver 0.72

To install the SDK tools & drivers in Windows 7 (and other versions?): [HOWTO] Install Google SDK and ADB drivers...

The following instructions are written on how to enter APX mode. To enter Fastboot and Recovery modes, simply follow the same instructions but use the Volume Down button. Once the message: "Checking for RCK.. press key <Vol_Up> in 5 sec to enter RCK" is displayed, follow the displayed instructions to enter the desired mode. Note: The screen remains blank in APX mode.

When your tablet is turned off, to enter APX mode:

Make sure your USB cable is connected to your tablet and PC. While pressing the Volume Up button, press the Power button for a few seconds, and then release both buttons.

Make sure the USB cable is not plugged into your tablet (but is connected to your PC). While pressing the Volume Up button, plug the USB cable into your tablet. Release the Volume Up button after a few seconds (modified from daws' suggested method).

When your tablet is up and running, to enter APX mode:

Turn your tablet off and wait a few seconds. Connect your USB cable to your tablet and PC. While pressing the Volume Up button, press the Power button for a few seconds, and then release both buttons.

Make sure your USB cable is connected to your tablet and PC. Open a command prompt on your PC, navigate to the folder containing adb.exe, type: adb reboot and hit the Enter key while holding down the Volume Up button until the screen remains blank for a few seconds.

From a tablet based terminal emulator, type: su and hit the Enter key, then type: reboot and hit the Enter key while holding down the Volume Up button until the screen remains blank for a few seconds. One suggested app (by tobdaryl) is the free Android Terminal Emulator from Google Play. Note: You must be rooted for this to work.

Press the tablet reset with a paperclip while pressing the Volume Up button until the screen remains blank for a few seconds (the reset is located about either 25mm or 1" below the sdcard slot). Note: Do not press hard!

When your tablet is in Fastboot mode, to enter APX mode:

While pressing the Volume Up button, press the Power button for 10 seconds. Release both buttons a few seconds after the screen goes blank. One variation is to wait and press the Volume Up button immediately after the screen goes blank and then release it after a few seconds. If you wait too long to press the Volume Up button, your tablet will just boot up normally.

Make sure your tablet has the USB cable connected to your PC. Open a command prompt on your PC, navigate to the folder containing fastboot.exe, type: fastboot -i 0x0B05 reboot and hit the Enter key while holding down the Volume Up button until the screen remains blank for a few seconds. One variation is to wait and press the Volume Up button immediately after the screen goes blank and then release it after a few seconds. If you wait too long to press the Volume Up button, your tablet will just boot up normally. Note: Newer versions of fastboot.exe do not require the "-i 0x0B05" option.

Or, as a last resort!

Remove your tablet's cover, disconnect the battery, press and hold the volume up button, and reconnect the battery!

The following instructions are written on how to switch from one mode to another (not covered above).

When your tablet is up and running, to enter Fastboot or Recovery mode:

Make sure your USB cable is connected to your tablet and PC. Open a command prompt on your PC, navigate to the folder containing adb.exe, type: adb reboot-bootloader and hit the Enter key. Once the message: "Checking for RCK.. press key <Vol_Up> in 5 sec to enter RCK" is displayed, follow the displayed instructions to enter the desired mode. Note: I was unable to verify this method possibly due to having the AndroidRoot.mobi custom bootloader. This method only performs a regular reboot for me.

From a tablet based terminal emulator, type: su and hit the Enter key, then type: reboot bootloader and hit the Enter key. Once the message: "Checking for RCK.. press key <Vol_Up> in 5 sec to enter RCK" is displayed, follow the displayed instructions to enter the desired mode. One suggested app (by tobdaryl) is the free Android Terminal Emulator from Google Play. Note: You must be rooted for this to work, Note2: I was unable to verify this method possibly due to having the AndroidRoot.mobi custom bootloader. This method only performs a regular reboot for me.

When your tablet is in APX mode, to enter Fastboot or Recovery mode:

While pressing the Volume Down button, press the Power button for 10 seconds. Release both buttons a few seconds after the screen goes blank. One variation is to wait and press the Volume Up button immediately after the screen goes blank and then release it after a few seconds. If you wait too long to press the Volume Up button, your tablet will just boot up normally. Once the message: "Checking for RCK.. press key <Vol_Up> in 5 sec to enter RCK" is displayed, follow the displayed instructions to enter the desired mode.

When your tablet is in Fastboot mode, to enter Recovery mode:

Make sure your tablet has the USB cable connected to your PC. Open a command prompt on your PC, navigate to the folder containing fastboot.exe, type: fastboot -i 0x0B05 reboot-bootloader and hit the Enter key. Once the message: "Checking for RCK.. press key <Vol_Up> in 5 sec to enter RCK" is displayed, press the Volume Up button within 5 seconds. Note: Newer versions of fastboot.exe do not require the "-i 0x0B05" option, Note2: I was unable to verify this method possibly due to having the AndroidRoot.mobi custom bootloader. This method only performs a regular reboot for me.

When your tablet is in Recovery mode (TWRP v2.3.x), to enter Fastboot mode:

Select the "Reboot" option and then select the "System" option while pressing the Volume Down button until the screen remains blank for a few seconds. Once the message: "Checking for RCK.. press key <Vol_Up> in 5 sec to enter RCK" is displayed, wait 5 seconds for the icons to appear, and follow the instructions to select/confirm fastboot mode. One variation is to wait and press the Volume Down button immediately after the screen goes blank and then release it after a few seconds. If you wait too long to press the Volume Down button, your tablet will just boot up normally.

When your tablet is in Recovery mode (TWRP v2.3.x), to enter APX mode:

Select the "Reboot" option and then select the "System" option while holding down the Volume Up button until the screen remains blank for a few seconds. One variation is to wait and press the Volume Up button immediately after the screen goes blank and then release it after a few seconds. If you wait too long to press the Volume Up button, your tablet will just boot up normally.