A) Double Tap your Home (guide) button which will enable snap mode, go to game dvr, then end now, then click on the appropriate time. If you are submitting a clip, I highly recommend 30 seconds or 1 minute.
B) Click Home button, either go to snap mode and follow the steps above or, if you have Game DVR pinned to your home (dashboard) click that and follow the same steps. I find it alot easier if Game DVR is pinned.
How to capture on SmartGlass
The following steps apply to both Windows 8.1 and mobile apps.
Make sure you have the most recent Smartlass update, which I believe is labelled as "BETA" on the thumbnail for the app.
Once the app is open, you should be on the Home screen, select the left tolbar and click home if unsure.
Also, make sure that the app is connected to your console, this can be checked at the top right, with the wifi/console icon furthest to the left.
Once that is done, keep the app open whilst playing and when you want to record something, click the black bar at the bottom which says "Destiny now playing"
Then click the record that button - this will record the last 30 seconds and the clip can be access by going to Game DVR in "My Games and Apps" or by snap mode then Game DVR - and then clicking on view my clips.
Although this may seem like a lengthy process, it is the only way of recording clips without capture card and without the game having a theatre mode.