Roaming is the facility that allows you to use your mobile phone whilst you are travelling in a different country. All UK networks have Roaming Agreements with other countries, some may suit your needs better than others. For example, unlike '3', O2 has roaming agreements with Botswana, Colombia and Monaco; however,'3' offers more coverage in the Caribbean than O2. So make sure that you check that you'll have the coverage you need by contacting your network provider.
You should also check that your mobile isn't barred from use abroad. A simple call to your Network Customer Support should unblock your phone if this is the case. It may take a few days for your service to work, so try to contact your network at least a week before you travel.
When you arrive, switch your mobile on. It will search for a network and, after a short time, automatically register onto an available one. However, if this doesn't happen, you may need to search for one manually. You'll find this facility under your phone settings; check your mobile's user guide for more details.
Many countries will allow you to dial directly from your mobile phone, without having to go through an operator. This will depend on your network provider and the type of contract you are on. When you make a phone call from these 'Direct Dial' networks, you will either need to simply dial the number as you would from home, or you may need to replace the initial 0 with the appropriate country code. For example, if you are calling the UK, instead of dialling (01234) 123123, dial +44 1234 123123. Again, check with your network provider for details.