Find a replacement action bar
The default Blizzard action bar sucks. That's really all there is to it. It doesn't support even the most basic features, and is so inflexible that it will undoubtedly hold you back. There's a ton of action bar mods out there, and most of them are robust enough to perform the tasks we're going to ask of them. I personally like Dominos, but I have several friends who prefer Bartender. Regardless of what addon you choose, it's important that you familiarize yourself with it and customize it as you see fit. It's important to play with a UI that works the way you do, so don't feel constrained to copy someone else.
The key to binding your keys properly is to sort your spells into different categories, and then making bars for each category of spell. The categories I like to use are: core spells, secondary abilities, lower priority spells, clutch / time-sensitive moves, and cooldowns. We also need to differentiate between keys on the keyboard, since every key is not created equal. Assuming you use W-A-S-D to move, the best keys are immediately next to those, the second best keys are two keys away, and the lesser keys are further away. We want to put our best spells on the best keys, and our worst spells on the worst keys.
The first bar & cheap WoW gold
I like to have my core spells on a single bar, and I center this along the bottom of my screen to provide a foundation that I'll build upon later. You want to keep your bread and butter spells grouped together for easy access. I keep these abilities on my first bar, in this order:Holy Light, Flash of Light, Holy Shock, Judgement of Light, Sacred Shield, Beacon of Light.
The second bar & buy WoW gold
Next, I like to build a second bar full of buttons, and these are the moves that I need access to on a regular basis, but they're not the highest priority and I usually know I'm going to use them ahead of time. I place things like Aura Mastery, Divine Plea, Hand of Sacrifice, and Hand of Salvation on this bar. I use the Shift key to access these spells, since I'm typically waiting to cast them at the right time, and I'll have plenty of time to press Shift and the proper key. You don't necessarily need to memorize the keybind for every one of these spells, but you should at least be able to quickly look and then press the right key combo to activate the spell.
The third bar & WoW gold
I throw all of the junk that doesn't really need to be bound on a large third bar, and these are spells that you don't use on a regular basis or that you would only use out of combat. This is where I put things like individual Blessings, Righteous Fury, Holy Wrath, Resurrection, Consecration, and Divine Intervention. It's important that you have these abilities on your bar somewhere, but they're so low-priority that you don't need to waste keyboard real estate by binding them. The key is knowing which spells can go on this bar, and which you should bind instead. I like to say that if I use a spell every time I'm in a raid, it deserves to be bound. If I only use it every few raids or in a very particular situation, I'm probably fine just clicking it when the time comes. I mean, will a shortly delayed Exorcism really cost me that much?
Time-sensitive bar & cheapest WoW gold
At first I tried to intersperse clutch spells throughout my other bars, but we just keep accumulating them and so I finally made a separate bar just for these. Most of them are bound to the high value keys, like Q, E, R, and F. These keys are the easiest to push, so you should put anything time-sensitive on one of these keys. I use the F and Shift F binds to handle both of my primary Hand spells, Freedom and Protection. Again, both of these are mouseover macros, since if I'm using Hand of Protection on someone, it usually needs to be quick.
The bottom row & buying WoW gold
It took me a really, really long time to bind anything to the Z key. I loved the ability to unsheathe my weapon on demand, which was great for both screenshots and showing off. However, thanks to the Valithria encounter, I finally found a button combo that made it worth giving that ability up. I now have a cast sequence macro that ties together Avenging Wrath (usually on my second bar), Divine Illumination (also a second bar move), and activates my Talisman of Resurgence. I push Z-Z-Z and I go from a meek holy paladin to a glowing beacon capable of healing massive dragons with a single cast.
Conclusion: While I can share with you how I have my key binds set up, these buttons only work for me because I'm used to them. Feel free to experiment and make up your own combinations, as long as you're working towards the goal of binding as many keys as possible. It may feel weird at first, but over time, it will make you a much better player. The longer you play with your keybinds, the more natural the feel to your hands. I am pretty sure I could play at about 95% performance with all of my bars turned off, and I frequently test myself in heroics by disabling them. It's one way to make an otherwise boring run through Azjol-Nerub interesting again.