How do I move my domain to another ISP?

This varies with the provider. If you have a reputable provider they will allow you to perform this action yourself. Some companies take it to heart when you try to move away from them and can make it a lengthily and costly experience. Some providers offer services such as free transfers for UK-based domains but generally when the domain is transferred it is also renewed for an additional year meaning cost is involved. Normally the transfer process takes 24-48 hours for UK-based domains whereas international domains (.com) can take up-to 7 days.