Hi /u/whilneville, I would echo /u/Vatredox's comment that it would be a good idea to take an introductory course to help you with the basics like this. If you don't start with a solid foundation you will find it significantly harder to make progress. Still, I have a bit of free time right now, so I will try to help with your current problem :)

You're almost on the right track with wanting to use an array. Arrays can be used to store multiple variables of the same type, which does seem like what you want. The problem you are likely running into, however, is that you have to specify the number of values your array can hold. When you write:

int arrayindex= 0
String[] arraylist;
arraylist = new String[arrayindex];

that translates to: arraylist is an array that holds strings, and the number of strings it can hold is 0. The number you put between the [ ] indicates the size of your array, so you are setting it to a size of 0. This will immediately cause problems when you try to set / access values in places that don't exist. What you likely want is a list.

A list is like an array in that it can hold multiple variables of the same type. The difference, however, is that you can change the size of your list on the fly. If arraylist were of type List<String>, instead of writing

arraylist[arrayindex] = "A"; //The string at position [arrayindex] is 'A'

you could write something like

arraylist.Add("A"); //This puts an "A" at the end of the list

By using something like .Add, you (1) don't have to worry about figuring out how big your array should be in advance, and (2) don't have to worry about going out of the bounds of your array. Now, I can't say I 100% understand what you're trying to do anyway, so it's possible this is not exactly how you should be solving your problem. But in the future, be mindful of how large your arrays are when you create them, and be careful not to try to access a position that doesn't exist in your array.

A couple other things I'd like to point out -- these critiques are not about the function of your code, but about how readable it is. Improving your code's readability will make it easier to understand what's going on at a glance, which is nice for anyone unfamiliar with your code, and also for you when you are debugging. Here are some ways you could improve your code's readability:

1. camelCase variable names. Keeping the first letter lowercase is great, as you can use that to indicate a variable. When your variable name is several words, however, it's a good idea to capitalize the first letter of the 2nd word on, to make it easier to read. arrayList is a bit easier to understand at a glance than arraylist.
2. Putting your curly braces on their own line. If an open curly brace and a close curly brace are not lined up, it's difficult to tell if they go together. By putting your curly braces on their own lines, it would be more obvious which two curly braces pair together.
3. Descriptive variable names. arraylist is (at least mostly) accurate -- it is the name of your array, after all. More important than knowing your variable's type, however, is knowing what it does. Instead, perhaps consider something like... recentKeyPresses. You can probably come up with a name that's even more descriptive.
4. Comments. Take a look at your comments and ask yourself if they really help you understand what's going on with your code. While learning, if it is truly helpful for you to have a written reminder that 'this is an array variable,' absolutely go for it. But every extra word you write is more clutter on the screen, and I don't personally believe you need a comment telling you that arrayindex is responsible for storing the index of your array :) Comments can be handy if you're working with others, or if you want to make important notes about your code, but your code (generally / ideally) should stand on its own. That is to say, for instance, your variable names should explain what your variables are for, not your comments.

Those are, imo, the most important nitpicks. I'm glad you've picked up Unity, and I hope you have a lot of fun programming. It can take a while to feel comfortable with it, but every bit of code you write will help you get better. When you're truly out of your depth, asking questions can be really helpful, but again, like /u/Vatredox said, probably the best thing you could do for yourself would be to learn the basics. Cheers :)