Ha did my kitchen a couple of weeks ago, I'm no expert just the victim of a the female need for having stuff painted every few years
As its the kitchen you'll need to clean the walls properly first, was them all down with sugar soap and again with clean water
Fill any holes with polly filler , sand off any rough patches
Any particular greasy areas try this
Krud Kutter its amazing stuff
If you've got any stains that need covering use a "Problem solving primer" this will stop the stain coming thru you lovely paint work
I would also apply at least one coat of standard white emulsion (unless you're painting in the same colour, in which case don't paint white first).
Paint the ceiling next as you'll probably get bits on the walls , which wont matter too much as you'll be painting them
User a roller for large surface areas, get your missus to cut in for you (the corners etc where the roller wont go)
If your glossing as well, do this last, sanding down and undercoating first (prob best to do the undercoating before you start painting the walls)
Don't get too much paint on your brush, about a quarter of the way down the bristles when dipping into the paint