I won't try to get you to elite play here (I'm not there myself), but a basic approach to DK rotation is...
(well first - make sure you have Infest glyphed so you can Plague Leach more often)
If you have runic power left from previous fight, pull with Infest.
Otherwise, drop a Defile (group) or run up and Death Strike (single target).
DS-DS-Infest-Plague Leach- DS
Defile or Blood Boil when you proc a free one (more often if trash group)
Death Coil whenever DS is on cd - it boosts your max health and generates charges for Blood Tap
Blood Tap at 5 or 10 charges for more Death Strikes
Prioritize Soul Reaper over other attacks once target is <25% (unless you need DS for survival)
Now obviously the above needs to adapt to the fight, your current health status, etc., but hopefully gives you some idea. DKs can feel very slow (rune depleted) if not managed well, but you can enjoy a LOT of uptime if managed correctly. I am still learning, but usually have highest activity level (as measured by Recount) in my group. At least I'm clicking lots of buttons. :P
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Oh - and KUDOS - for being humble to put yourself out there like this, inviting feedback, taking it well, and so on. Always great to see someone humble and eager to improve!