2 unconfirmed transactions for over a week now. How do I push these through?

I have 2 transactions that have been unconfirmed for over a week. I am trying to send some btc to my mycelium wallet for spending etc and I accidentally sent the first transaction with no fee and apparently the 2nd transaction with too low of a fee?I have seen people mention "do the same transactions over again with a higher fee" but that makes no sense to me at all. Wont that just send new bitcoin and have have nothing to do with the stuck transactions? Can someone ELI5 this for me?Also, what should I be entering as a standard fee in the core wallet so I can prevent this from happening again?Thank you via /r/Bitcoin http://bit.ly/28SxE9s