After the introductory cutscene, you'll be left in control of the Prince. Follow Elika along the canyon, using the same moves as she does to traverse any obstacles. If you haven't turned off tutorials in the options screen, you'll be given on-screen prompts showing the exact buttons to press, and even when to press them.
Jump across the first two gaps, or drop down and jump up to the second platform. The next set of gaps are longer and deeper, so you've got to wallrun - jump at an angle towards the sections that look scraped and scored and the Prince will automatically run along a short distance, landing on the other side of the gap.
Climb up the ledge then jump across to the platform just below the pair of guards. To get to the next platform, wallrun along the scraped section of the wall, and jump at the end of the run. On the other side, follow the path and you'll catch up to Elika, who's been cornered by a more guards.
Combat in Prince of Persia is all one-on-one, so you've only got to fight one guard at a time. Again, the tutorial prompts will give you a pretty straightforward way of defeating the first guard. It's advisable to knock him against any wall surrounding the combat area - following the tutorial prompts should lead you to do this automatically, unlocking the Up Against It achievement or trophy. The second guard will be dealt with by Elika in a short cutscene after the fight, then you're back in control.
Follow Elika up the walls, using the wallrun, jump, wallrun method she demonstrates, then keep going along the canyon after her. There's a short gap you can easily jump over, then wallrun around the corner, jumping at the end to land on solid ground. Around to the left, wallrun on the left wall, jumping to the right wall at the end of the first section to wallrun to the next platform.
There'll be another short cutscene in which the guards try to drop a stone pillar on you - it takes out the bridge you're on, but Elika uses her magic ability to save you from the fall.
That helpful save has weakened her, so you'll have to carry Elika for a little while. She'll tell you that she needs to get to the temple, and after a short distance insist that you let her down. Here, you've got to fight another guard. As before, follow the on-screen prompts to defeat him, or just attack using your own techniques. Be sure to use the block and deflect buttons; while these enemies aren't very tough, the practice you get here will be very helpful against some of your later opponents.
When he's been dealt with, Elika will have recovered enough strength to walk; you can now speak with her to learn more about your current location or objective.
Climb up the short wall in front of you, then jump across the gap. Wallrun and jump to the next platform, then use another wallrun to get to the next bit of solid ground. You'll need to wallrun, then jump to the canyon's opposite wall, wallrunning further, then jump as you get to the end, landing on a platform with another guard to fight. He's followed immediately by a larger opponent able to take more punishment, but still won't present a serious challenge to the Prince.
Into the temple
Gripfall down the cliff face and you'll find yourself standing at the edge of a wide desert, with an impressive-looking, if overgrown, temple in the middle. Follow Elika across to it, but instead of going up the stairs to the temple, go all the way around to the side farthest from the cliff you just came down. You'll find a small corridor in the rock here; follow it to the bottom for an achievement or trophy.
Go back to the temple and up the steps to where Elika's waiting, then jump up the wall to the ledge. Move as far right along the ledge as you can, then wallrun up again to the fissure. Climb it then jump to the very top of the platform.
At the top, grab either end of the crank and turn it anti-clockwise to open the door. Gripfall back down the wall you just climbed and enter the door to the temple, following the corridor to the end. Activate the ring switch at the end to open the door into the temple's main room, then go down the slope to your right (or just jump forward off the raised platform) to reach the glowing tree in the middle of the room.
You may have defeated the king, but he's still able to do what he came for - he cuts down the Tree of Light, releasing the God of Darkness, Ahriman, from his thousand-year prison.
The first obstacle you face in the rapidly-collapsing temple is one of Ahriman's soldiers. You can now use Elika's magic attacks in combat, which is particularly effective against these corrupted enemies. For a quick kill, push him against one of the walls around the combat area or towards the edge - the Prince will finish him off with a killing blow, or push him into the pit below.
Jump across the platforms, then wallrun and jump to another wallrun, which leads to a ledge cut into the wall. Follow that to the left, then wallrun again and jump to the solid ground. Jump across to the slope on your right, following it up to the door you used to enter the temple, jumping across at the top to fight another of Ahriman's soldiers. Defeat him the same way you dealt with the last one, then head into the corridor.
It's important to take this section slowly - despite the dramatic music and Elika's insistence, this bit has no time limit. If you move too hastily down the corridor, the floor can collapse underneath you - and while Elika's there to save you from certain death, if you want the "Be gentle with her" achievement then you need to minimise her rescues.
Keep an eye out for wallrun sections, but be aware that you'll sometimes have to jump from the wall back to a platform. The final jump in the section is too great for the Prince to make on his own, but you can use Elika to extend the distance you jump - if the tutorial is still on, it will prompt you to press the button just after you jump with the Prince.
The Fertile Grounds
Outside the temple, Elika will explain the map on the ground, and points out the four areas currently accessible to you. You can tackle them in any order; if you bring up the map and set any of them as your destination, you can then use Elika to show the way - follow the glowing trail to your destination.