What must I do to make my methods awaitable?

Your method

private async Task TestAsyncAwait()
{
    int i = await TaSLs_Classes.TASLsUtils.GetZoomSettingForDistance(5);
}

should be written like this

private async Task TestAsyncAwait()
{
    Task<int> t = new Task<int>(() =>
    {
        return TaSLs_Classes.TASLsUtils.GetZoomSettingForDistance(5);
    });
    t.Start();
    await t;
}

If you need to return the int, replace the Task type:

private async Task<int> TestAsyncAwait()
{
    Task<int> t = new Task<int>(() =>
    {
        return TaSLs_Classes.TASLsUtils.GetZoomSettingForDistance(5);
    });
    t.Start();
    return await t;
}

You only need to return an awaitable. Task/Task<TResult> is a common choice; Tasks can be created using Task.Run (to execute code on a background thread) or TaskCompletionSource<T> (to wrap an asynchronous event).

Read the Task-Based Asynchronous Pattern for more information.