You can't just access Heroic versions of raid bosses automatically. You need to have killed the endboss of a given raid on regular to toggle Heroic for the instance. That's your biggest gateway. If you're at the point where you're comfortable doing a full clear on regular, you're probably ready to start the earlier bosses on Heroic.

As Sidone said, Halfus is a good place to start. There are no new mechanics for the fight: the only difference is that all five adds are active, instead of having two inactive. Your raid should already be familiar with how everything works; you just need to figure out how to deal with everything at once. My guild leaves Slate down but pops everything else, pretty much right away, using Tricks/MD to get everything to the tanks. (We wait a few seconds to release the whelps, so that I can establish initial aggro on Storm.) I take Storm, Nether, and the whelps; the other tank takes Halfus and Time. We burn Lust/TW as soon as the whelps are out, at which point we kill Storm > Time > Nether > Halfus. (The whelps go down through incidental AOE.) We BOP off the initial stack of Malevolent Strikes when it gets high (usually 10-15); Storm should be dead by the time the stacks get back up into the 6-9 range where we need to start swapping. After that, we trade Halfus and redistribute remaining drakes as necessary until everything is dead. The one downside to using two tanks rather than three is that you sometimes get really bad RNG at the beginning of the pull with MS stacking, which will pretty much guarantee a wipe. We've found it's worth it for the extra DPS, though.

A note of caution: the requirements for 10-man raids in the current tier are very tight. Because of the way the fights are designed and balanced, there is frequently only one "right" way to kill a boss. Making a simple change can be the difference between endless wipes and comparatively easy success. The Wrath model where 10-man was usually easier than 25 no longer holds, at least for now.