One of the most important things is to make little promises and keep them. Like if you promise to do some household work every Sunday, try to do it consistently. When you show that you are reliable and can be trusted on these small things, you are slowly but surely demonstrating that you can be trusted on bigger things too.
Your girlfriend or wife is going to need constant reassurance that you have changed. This means that you are going to need to apologize more than once over time.