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I looked at the R2D2 instructions on my EV3 home edition software but I don't have all the parts necessary. 2 of the parts I don't have are the infrared sensor and remote infrared beacon. Now I figured that if I am to program a robot that will follow me without these 2 components, I would use the ultrasonic sensor, which I do have as a substitute. But then I would probably also need to use the color sensor and I have no idea how my pale skin color would show up when programming the color sensor(probably black because it doesn't recognize it but I don't know).

And how could I get it to climb stairs? I guess I could use the 2 large motors as a source of a pulling force that will pull the whole robot upwards but is there a better way?

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Sounds like an ambitious project. I would split it up into two stages.  The EV3 expansion set allows you to build a stair climbing robot - you can use their instructions or build something similar to it. 

As for the follower function, the color sensor has a very short range, so you (or your color sample) would have to be very close to the robot to be detected. The ultrasonic sensor would be the better option, but it also has limited range, although it is better than the color sensor. The problem with using this sensor is that it can't tell the difference between your leg and a wall, so you'd be limited to using it in open, clear areas. The sensor would also need to sweep the area to find your position, limiting the speed at which you can walk.

The best solution is to indeed use the infrared sensor and beacon. The robot does a sweep, locates the target and drives to it. The cycle is then repeated. 

You can probably incorporate the follower function into the stair climbing robot. 

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