What Makes a Method Thread-safe? What are the rules?

It must be synchronized, using an object lock, stateless, or immutable.

link: http://docs.oracle.com/javase/tutorial/essential/concurrency/immutable.html

If a method (instance or static) only references variables scoped within that method then it is thread safe because each thread has its own stack:

In this instance, multiple threads could call ThreadSafeMethod concurrently without issue.

public class Thing
{
    public int ThreadSafeMethod(string parameter1)
    {
        int number; // each thread will have its own variable for number.
        number = parameter1.Length;
        return number;
    }
}

This is also true if the method calls other class method which only reference locally scoped variables:

public class Thing
{
    public int ThreadSafeMethod(string parameter1)
    {
        int number;
        number = this.GetLength(parameter1);
        return number;
    }

    private int GetLength(string value)
    {
        int length = value.Length;
        return length;
    }
}

If a method accesses any (object state) properties or fields (instance or static) then you need to use locks to ensure that the values are not modified by a different thread:

public class Thing
{
    private string someValue; // all threads will read and write to this same field value

    public int NonThreadSafeMethod(string parameter1)
    {
        this.someValue = parameter1;

        int number;

        // Since access to someValue is not synchronised by the class, a separate thread
        // could have changed its value between this thread setting its value at the start 
        // of the method and this line reading its value.
        number = this.someValue.Length;
        return number;
    }
}

You should be aware that any parameters passed in to the method which are not either a struct or immutable could be mutated by another thread outside the scope of the method.

To ensure proper concurrency you need to use locking.

for further information see lock statement C# reference and ReadWriterLockSlim.

lock is mostly useful for providing one at a time functionality,
ReadWriterLockSlim is useful if you need multiple readers and single writers.

There is no hard and fast rule.

Here are some rules to make code thread safe in .NET and why these are not good rules:

1. Function and all functions it calls must be pure (no side effects) and use local variables. Although this will make your code thread-safe, there is also very little amount of interesting things you can do with this restriction in .NET.
2. Every function that operates on a common object must lock on a common thing. All locks must be done in same order. This will make the code thread safe, but it will be incredibly slow, and you might as well not use multiple threads.
3. ...

There is no rule that makes the code thread safe, the only thing you can do is make sure that your code will work no matter how many times is it being actively executed, each thread can be interrupted at any point, with each thread being in its own state/location, and this for each function (static or otherwise) that is accessing common objects.

If a method only accesses local variables, it's thread safe. Is that it?

Absolultely not. You can write a program with only a single local variable accessed from a single thread that is nevertheless not threadsafe:

https://stackoverflow.com/a/8883117/88656

Does that apply for static methods as well?

Absolutely not.

One answer, provided by @Cybis, was: "Local variables cannot be shared among threads because each thread gets its own stack."

Absolutely not. The distinguishing characteristic of a local variable is that it is only visible from within the local scope, not that it is allocated on the temporary pool. It is perfectly legal and possible to access the same local variable from two different threads. You can do so by using anonymous methods, lambdas, iterator blocks or async methods.

Is that the case for static methods as well?

Absolutely not.

If a method is passed a reference object, does that break thread safety?

Maybe.

I've done some research, and there is a lot out there about certain cases, but I was hoping to be able to define, by using just a few rules, guidelines to follow to make sure a method is thread safe.

You are going to have to learn to live with disappointment. This is a very difficult subject.

So, I guess my ultimate question is: "Is there a short list of rules that define a thread-safe method?

Nope. As you saw from my example earlier an empty method can be non-thread-safe. You might as well ask "is there a short list of rules that ensures a method is correct". No, there is not. Thread safety is nothing more than an extremely complicated kind of correctness.

Moreover, the fact that you are asking the question indicates your fundamental misunderstanding about thread safety. Thread safety is a global, not a local property of a program. The reason why it is so hard to get right is because you must have a complete knowledge of the threading behaviour of the entire program in order to ensure its safety.

Again, look at my example: every method is trivial. It is the way that the methods interact with each other at a "global" level that makes the program deadlock. You can't look at every method and check it off as "safe" and then expect that the whole program is safe, any more than you can conclude that because your house is made of 100% non-hollow bricks that the house is also non-hollow. The hollowness of a house is a global property of the whole thing, not an aggregate of the properties of its parts.