Ninja Gaiden is a linear action game, in which you must guide the ninja Ryu Hayabusa through six "Acts" that comprise 20 levels. You may not select or skip any level; to complete the game, you must play every stage in order. At the end of each Act, you must challenge and defeat one or more bosses. If you lose this fight, you may be sent back to an earlier moment in the Act.
Throughout your adventure, there are a couple of techniques that you can make use of to advance further throughout the game.
When Ryu jumps towards a wall or column, he will grab a hold of the side and cling to it. He will not fall or slide down, and you can remain there indefinitely (time permitting). You can use this technique to evade the attacks of enemies and bosses alike.
If Ryu is located between two walls in close proximity to one another, he can jump back and forth between them, and use them to reach higher locations than he could otherwise normally reach. To do so, you can hold down the jump button ( on the NES) while pressing and to leap back and forth between the two walls. You are not required to release the jump button between leaps.
The wall hop technique allows Ryu to climb higher off the ground with the aid of only one wall instead of two. To perform this technique, you must jump towards and cling to a wall. From there, hold the jump button down, push away from the wall, and then immediately push back towards the wall. For example, if you jump left to grab a wall, hold down jump, push right on the control pad, and then immediately push left as soon as you let go of the wall. If done correctly, you should actually be able to rise and cling to the wall higher than you were when you started. Do this correctly multiple times, and it is possible to climb to the top of the screen.