Introduction
I don't play holy paladin, but I have a reasonable understanding of their rotation and of the game in general.
As others have said, more information is required to be able to answer this question fully. A link to your character's profile would be a good start. The most likely reason for your healing being lower than others and running out of mana is gear.
It is also not clear whether you are raiding in 25 man rf, flex, norm or hc. I assume 25 man from the mention of being below the top three healers on recount.
Strategy (or rotation)
This is commonly called rotation to differentiate it from the overall plan of the raid group.
putting beacon of light on the off-tank is situational and should not be done without thought. Particularly in RF, one tank may end up tanking the boss throughout, if there is not a mechanic that forces a switch. In all difficulties, though, there are fights where there is a significant time period between each tank switch, the current off-tank takes negligible damage and the current tank takes heavy damage. In such cases, put your beacon on the current tank in addition to healing him to maximise throughput.
rather than spamming your cheap heal, focus instead on performing a full rotation. Holy Light is a filler, not a priority (I think you understand this, but it's worth emphasising).
the previous points apply here also.
it may be worth choosing Light's Hammer from your final tier and using that in AoE situations.
Look at http://www.noxxic.com/wow/pve/paladin/holy/heal-rotation-and-cooldowns for an easily-understandable introduction to playing holy paladin at a raiding level. Reading and enacting Noxxic's advice is likely to solve or significantly reduce the difficulties you are having (dependent on your gear).
If you want more details, there are plenty of sites such as http://forums.elitistjerks.com/index.php?/forum/141-paladins/ with existing advanced discussions of the class.
Overhealing
This is probably partly a consequence of leaving your beacon on the current off-tank. It's probably also partly due to the fact your focus is healing the tank in 25 man, where there will typically be large amounts of overhealing occurring (as opposed to AoE-oriented healers).
Position on meters
One thing to check is that you are looking for healing and absorbs on the meters. Looking just for healing will heavily bias it away from holy paladins and disc priests.
Meters don't tell the whole story, even if they are showing what you're expecting.
You're right to conclude that being significantly below the top three healers in the raids you join is something to work on, though.
Running out of mana (OoMing):
This is likely to be a matter of playing your rotation better, but it's also likely to be related to gear (spirit really makes a significant difference).
Be careful when casting holy radiance as this consumes a significant portion of your mana.
Although you don't mention it, I imagine you already make sure that
you are fully self-buffed, especially with seal of insight.
Divine Plea has been changed so that it no longer reduces the healing you
do. Depending on the fight, it may be sensible to use it first at 80%
mana and thereafter as soon as it comes off cooldown.
If possible, ask druids to Innervate you (if they don't need it themselves) and
make sure you stay within 40 yards of a shaman's Mana Tide Totem or a
priest singing Hymn of Hope.
If you continue having mana issues, a last resort can be casting only
when it is vital do so to stay keep a raid member alive or you have
Holy Shock/Eternal Flame available. This is clearly not a long term solution, but may be necessary if you are very undergeared.
Consider using the Glyph of Lay on Hands for an additional emergency mana regen.
Also, keep both Master Mana Potions and Potions of Focus on hand and
use each as appropriate.
