How do I abort/cancel TPL Tasks?

You can't. Tasks use background threads from the thread pool. Also canceling threads using the Abort method is not recommended. You may take a look at the following blog post which explains a proper way of canceling tasks using cancellation tokens. Here's an example:

class Program
{
    static void Main()
    {
        var ts = new CancellationTokenSource();
        CancellationToken ct = ts.Token;
        Task.Factory.StartNew(() =>
        {
            while (true)
            {
                // do some heavy work here
                Thread.Sleep(100);
                if (ct.IsCancellationRequested)
                {
                    // another thread decided to cancel
                    Console.WriteLine("task canceled");
                    break;
                }
            }
        }, ct);

        // Simulate waiting 3s for the task to complete
        Thread.Sleep(3000);

        // Can't wait anymore => cancel this task 
        ts.Cancel();
        Console.ReadLine();
    }
}

This sort of thing is one of the logistical reasons why Abort is deprecated. First and foremost, do not use Thread.Abort() to cancel or stop a thread if at all possible. Abort() should only be used to forcefully kill a thread that is not responding to more peaceful requests to stop in a timely fashion.

That being said, you need to provide a shared cancellation indicator that one thread sets and waits while the other thread periodically checks and gracefully exits. .NET 4 includes a structure designed specifically for this purpose, the CancellationToken.

Like this post suggests, this can be done in the following way:

int Foo(CancellationToken token)
{
    Thread t = Thread.CurrentThread;
    using (token.Register(t.Abort))
    {
        // compute-bound work here
    }
}

Although it works, it's not recommended to use such approach. If you can control the code that executes in task, you'd better go with proper handling of cancellation.

Aborting a Task is easily possible if you capture the thread in which the task is running in. Here is an example code to demonstrate this:

void Main()
{
    Thread thread = null;

    Task t = Task.Run(() => 
    {
        //Capture the thread
        thread = Thread.CurrentThread;

        //Simulate work (usually from 3rd party code)
        Thread.Sleep(1000);

        //If you comment out thread.Abort(), then this will be displayed
        Console.WriteLine("Task finished!");
    });

    //This is needed in the example to avoid thread being still NULL
    Thread.Sleep(10);

    //Cancel the task by aborting the thread
    thread.Abort();
}

I used Task.Run() to show the most common use-case for this - using the comfort of Tasks with old single-threaded code, which does not use the CancellationTokenSource class to determine if it should be canceled or not.