Sure, this takes a lot of random/CtA BGs, but presumably you want these weapons because you want to PvP with them.
"There is a pervasive myth that making content hard will induce players to rise to the occasion. We find the opposite. " -- Ghostcrawler
"Almost every time I have gotten to know a critic personally, they keep up with the criticism but lose the venom." -- Ghostcrawler
"Nothing will ever be attempted if all possible objections must first be overcome." -- Samuel Johnson
It's a PITA to get started this season, but it can be done
Assuming you have no PvP gear the best place to actually start imo is by either getting some friends to farm dungeons or queuing as tank and getting the quick queue. This way you will get 120 JP per boss kill, 500 JP = 250 honor and the dungeons take about 10mins to complete. I think all dungeons have at least 3 bosses so you actually get honor pretty quick.
This way you wont be absolutely owned when you first jump into random bg's or feel like you can't kill anything or thinking damn i just wasted 25-30mins getting trounced!
Then as other people mentioned its all about reading up, setting keybinds, ui etc.
Currently doing this for my feral druid got head/gloves/legs/shoulders/chest today, then all the other pieces tomorrow!
I chose to boost a DK to 90 and it's the most fun I've had in PvP for ages. Still learning the class but found two very helpful guides for unholy and frost and Arena Junkies. They had more than just the standard glyph/talent/stat priority most guides have including the closest thing to a priority system I've found and also had useful macros and comp advice. Gives a great base however almost everything in PvP is situational and you only really learn by playing. As you have experience as a DK (rune system, dot tracking etc.) you'll probably learn pretty quickly, good luck.