Get informed about the matter. Being seriously informed means reading all available information, including those sources of information which suggest it isn't as big an issue as suggested, or not an issue at all. -Read the critics-, not just the critics of the critics, or you'll find yourself confronting arguments you're utterly unfamiliar with, and may in fact make people -less- convinced.
If you can't get seriously informed, -don't talk about it-. You only do the cause harm by spreading poorly-understood or outright false information. Be prepared to speak to skeptics, which requires knowing what skeptics -actually- believe, as opposed to what ideologues strawman them as believing - even if you're not wanting to convince skeptics, you need to be able to deal with them in the context of talking to other people.
Divorce the information and issues from politics, as several have mentioned. Be cautious of bringing up potential solutions, because many are mired in political bullshit. Some of the more politically neutral solutions include nuclear power (and to a lesser extent hydroelectric and tidal harnesses), switching from coal to natural gas (beware making the perfect the enemy of the good), and a revenue-neutral carbon tax. Non politically neutral solutions include wind and solar power, "local" goods, and carbon credits.
Be aware when discussing the issues that all potential solutions do in fact have costs. If you think a particular solution is all good and has no or negligible costs, you're uninformed about that solution.
Also be aware that many people who believe global warming is a problem -also- believe that the cost of doing something about it may be higher than the cost of letting it happen - again, be informed, and be prepared to address their concerns, if only because they may be in the company of those you are trying to convince.
Beware of the broken window fallacy - replacing a power plant is an economic loss, it is wasted resources. Focus on -optimizing- the use of existing resources. It may be better to let a coal power plant run and replace it with something better when its lifespan is exhausted than to replace it immediately; yet again, be informed.
Also beware of first-world or middle-class bias. For much if not most of the world, the cheaper power that is coal electricity may be seen as more valuable than a slightly cooler earth. You may be able to afford more expensive electricity - the fact that -you- can afford it doesn't mean that everybody can. Treat other people's concerns with care.
And finally, this was written by somebody who believes that the evidence for global warming is dubious at best, and has seen quite a lot of the data manipulation that takes place. If you can't be at least as respectful as I am towards those who disagree with you, don't talk about it at all, or again, you'll do your cause more harm than good. Most of us skeptics became skeptical because of the blatantly unscientific behavior of ideologues. Don't repeat their mistakes.