If your running shoes are causing issues such as blisters or rubbing in an area of your foot, it is possible that re-lacing them could help solve the problem. If not, look for new shoes – there is no reason that you need to live with pain from running shoes.
(For a short triathlon, you probably want to avoid tying altogether with a nifty elastic system, but for training and longer triathlons you may choose to stick with tying laces).
Instead of trying to reinvent descriptions and pictures, here are two resources that provide a number of different examples of solutions for different issues. REI and the Happiest Blog.
I have used a method for heel slippage that worked quite well (pictured below).