HTC Explorer can be rooted using the Superuser script that it's available from XDA Developers forum. In order to root the phone you will need HTC Sync, an unlocked bootloader and Superuser script plus a recovery image since you will be going into Recovery mode to perform this operation.
First you will need to download the recovery package and run the recovery.bat file in fastboot mode (press the Volume Download + Power and choose FastBoot mode). Once this process is complete, reboot the phone in the Recovery mode and use the "install .zip from sd card" option and select Superuser.zip file after you place it in the root of the SD card. Wait for the process to finish and you will have a rooted phone.
