While all Hunter specs are getting some significant changes to their rotations, Survival is throwing practically everything out and starting anew, now that it's a melee spec (also making Hunters the third class - after Shamans and Druids - to have both melee and ranged dps specs.)
Survival will still have a pet, and they'll fight with a polearm (or potentially a staff at lower levels - the Survival artifact is a polearm.) Survival is keeping traps, which will actually be exclusively their domain.
Also, all Hunters are going to get much faster focus regeneration. I believe they're bringing it up to 10 per second before haste, which makes it identical to Energy, if I recall correctly.
So let's break down the core abilities:
Flanking Strike causes both you and your pet to attack the target. If the target is attacking you, the pet will deal an additional 50% damage and generate increased threat, and if not, you'll do 50% more damage. This costs 50 Focus and is on a six-second cooldown.
Raptor Strike costs 25 Focus with no cooldown, and looks like it will be the main way you burn off excess Focus if you have more than you need.
Mongoose Bite looks like it will be at the center of the rotation. It's a melee strike with 3 charges on a 10-second recharge. Each Mongoose Bite used within 3.5 seconds of the previous one will deal 50% additional damage, stacking up to 6 times. So for a quick burst you can blow all the charges in a row, or you can try to weave them in and out to try to maintain those stacks as long as possible. There's no Focus cost here - you're just going to have to balance the recharge and the buffs.
Hatchet Toss is a ranged instant attack with no cooldown, which I suspect you'll use when you can't get into melee range.
Harpoon is a ranged ability on a 15-second cooldown that shoots you toward the target and roots them for three seconds - it's your beginning-of-combat charge or gap-closer.
Laceration is a 12-second bleed on a 10-second cooldown that costs 35 Focus - clearly something you'll just want to maintain on the target.
Carve is a 40-Focus attack that does damage to enemies in front of you - rather simple AoE there.
Explosive Trap remains for Survival as the main damaging trap. Trap Launcher is now basically baked in to all traps, and all traps share a 1-minute cooldown.
Aspect of the Eagle appears to be your main damage (2-minute) cooldown. It increases you and your pet's crit chance by 10% and gives you 100% chance to gain charges of Mongoose Bite - I assume this is in addition to the Mastery, which might enhance a passive that you get before level 80.
Mastery: Hunting Companion will give your pet's attacks a (small) chance to give you charges of Mongoose Bite.
So my basic take on this is: (and remember that I'm not a theorycrafter - this is just my basic impression of what you're supposed to do with these abilities.)
1. Explosive Trap
2. Maintain Laceration
3. Use Flanking Strike on cooldown
4. Use Mongoose Bite if you're capped on charges or if the buff is within a second of falling off.
5. Use Raptor Strike.
During the testing phase, I'd keep a close eye on Mongoose Bite, as I think there could be some serious iteration on it. Also bear in mind that talents and artifact traits will add more buttons to the rotation. This is the absolute bare-bones of what the spec has going on.