Bitcoin transaction has been unconfirmed for over 24 hours... What should I do? I'm pretty new to Bitcoin and although the technology is pretty exciting, I feel as though the sluggish confirmation times are letting it down... 

On 18th December I instructed a Bitcoin transaction (5314fb75a5d08caf563cd6f6aaf40f448e9a9c6e0ba6affa499accd3534b97f6), admittedly with a pretty low fee, but I still wasn't expecting it to take days to get confirmed... Will this soon be dropped from the mempool or is there a way I can accelerate the transaction confirmation process? 

Yours,
citygent
It will be dropt from the mempool if it stays unconfirmed for a long time. If the fee is low, it takes more time to get confirmed. And just now the Bitcoin network is getting spamed by Bcashers. I would wait until the spam is over, and then put a fee in acordance to the time you are willig to wait until the confirmation.