'And' and 'That' are two overused words. But what are your options?
To take 'that' first, simply remove it as often as possible. If you can eliminate 'that' from a sentence and it still makes sense, leave it out. Simples!
'And' is a whole different problem as it's usually needed. There is a solution though: use different words. Which ones? Try these for a start:
There are more options at Random Thought's blog. Alternatively, create your own and remove those 'ands' from as much of your book as possible.
Go on, you know you want to.