The best way to use Beacon of Light is to always use Beacon of Light. Try to keep it up as often as possible. The mana cost of Beacon is not so high that it's untenable to keep it up at all times, and if you're using Glyph of Beacon of Light, it's even easier to do. Make sure Beacon is active while you're killing trash, active on every boss encounter, and I even keep it active during raid downtime. Managing buffs is part of playing a holy paladin, and so learning to juggle them becomes a top priority. I suggest getting a tracking addon like CLCBPT to monitor your Beacon duration and even keeping track of your Beacon uptime via a log parser like World of Logs.
Beacon has a relatively low mana cost when amortized over its duration, and even in a worst-cast scenario, it can never hurt to have it up. The best-case scenario is that you do double the healing and save everyone's life. You can recoup the cost of casting Beacon if it saves you just two Holy Lights, which means that you're really always saving mana. While it may seem like you don't always need Beacon, it's better to be safe than sorry. Good habits come through practice.
If you're supposed to be keeping Beacon of Light up, the next question becomes who to use it on. The easy answer is that you usually want to drop this on the tank. In a raid environment, there are usually two tanks, and so you can coordinate with the other healers as to which tank should receive Beacon. In a smaller dungeon or heroic environment, where you only have one tank, they're the obvious choice. You want to put it on the player who will be at less than full life the most often, as that's the best way to ensure the Beacon heals are actually productive. Also, since Beacon heals can be transferred at a distance of 60 yards, you'll want to put Beacon onto any tank that will be running around a lot. A great example is the tank facing Prince Keleseth of the Blood Prince Council.
However, just because tanks are the de facto first targets for Beacon, there are several other use cases that make sense in certain situations. This is particularly true for 5-mans, where you're often the only healer available. In situations where your life is at risk, it can actually be smarter to use Beacon of Light on yourself, like I did on Marrowgar. If the healer dies, the tank will die, and the group will die shortly after. While Divine Shield and our other defensive cooldowns can help us mitigate some of the incoming damage, sometimes it's simply easier to Beacon ourselves and keep healing everyone else. The tank will be able to survive the incoming damage without Beacon, since other healers are obviously capable of healing these encounters. A few good bosses that I like to Beacon myself on are The Black Knight in Trial of the Champion and Marrowgar in Icecrown Citadel.
Swapping beacon around
While it may seem like a good idea to swap your Beacon around to handle spells like Marked for Death or Mirrored Soul, it's usually not in your best interest to. It costs a ton of mana to be recasting Beacon before the duration expires, and it costs you a critical global cooldown when you have multiple targets taking damage. You're better off using that time to cast a heal on them, since they'll be needing it soon. Debuffs like this don't have long durations either, so it's not like you'd be getting the full benefit of Beacon of Light anyway. Save Beacon for targets that will need it for more than a few seconds, and just heal those people who will be taking damage. A great example would be targets afflicted by Mark of the Fallen Champion on the Deathbringer Saurfang encounter. They'll be taking damage for a long time, so putting Beacon on them makes sense.
Beacon, ultimately, is a proactive spell. If you want to use it properly, you need to know who you're casting it on and when to move it around. It's not something that you want to be focusing on in the moment, and you should plan its usage. However, if you do use your Beacon properly and you keep it up on the right targets, Beacon will be your greatest asset. It's what sets holy paladins apart from every other healer, and it gives our class more flavor than any of our other abilities. On fights like Valithria and combined with Glyph of Holy Light, it makes holy paladins even more powerful than ever. While Beacon is seeing a retooling in Cataclysm, I am hoping that it continues to be our signature move.
The Light and How to Swing It (Holy Edition) is dedicated to helping holy paladins become the powerful healers that we're destined to be. If you're new to the paladin's healing ways, you can learn the ropes with our Holy 101 article. We also have information on how to keep a tank alive, how to heal a raid when necessary and how to beat the GCD. Tanking is a job, DPS is a craft -- but healing is truly an art.