I've noticed that it's a little harder to get the phone to boot into HBOOT on the Evo 3D compared to the Evo 4G (and possibly other older HTC phones). The first and essential step is to first disable fast booting if it's enabled. To do that:
Go to Settings > Power > Fast boot (uncheck the box)
Here's how HTC phones traditionally boot into HBOOT:
Power off the phone. Wait 15 seconds or so after you see the screen go completely dark to ensure the phone is completely off. Then hold POWER + VOL-DOWN buttons together until the white HBOOT screen appears. If this worked for you, you're done and can skip the rest of this post.
If the traditional way did not work for you, here are the steps to get to HBOOT:
1) Charge your phone (not essential, but the LED will come in handy if you're not used to this procedure)*
2) Power off the phone by holding the power button. Wait for the popup menu to appear, then tap 'Power off."
3) Here's where the charging LED comes in handy. It will go off. Wait for it to come back on. When it does, the phone is fully shut down.
4) Press POWER AND VOL-DOWN and hold both down. Doesn't matter what order.
5) after 1 second (or longer), release only the POWER button. The charge light should go off.
6) Continue holding VOL-DOWN until the white HBOOT screen appears. If you let go of VOL-DOWN too early, nothing will happen. Go back to step 5 and repeat.
On the Evo, HBOOT will come up if you just keep both buttons depressed. Now, you need to let go of power button and continue holding VOL-DOWN. Now that you know roughly how long it takes for the phone to react, you can do the same thing without the phone charging.
*NOTE: some people have reported that when their phone is charging, they can't get into HBOOT no matter what they try. If it still doesn't work for you, try the above procedure without your phone being charged.
The good thing about science is that it's true whether or not you believe in it. -Neil deGrasse Tyson