Working memory (WM) and attention are interrelated, as a precondition for WM to operate is attention. In addition to attention we need awareness. The general view is that WM is explicit - conscious - and never implicit. The key difference between the term "working memory" and the older term "short-term memory", is precisely highlighting the role of attention and updating in memory.
To answer your question, we should consider that there are different types of attention. We can distinguish between momentary "spot-light" attention (or we could speak of "selective attention") and sustained attention (vigilance). In addition to WM training, there are training tasks for improving sustained attention. These are distinct put overlapping domains.
Unfortunately, the n-back task that was recommend in another answer varies due to different designs of the task and a score is therefore not easily comparable to other n-back scores, but for the same task only. One important distinction can be made between tasks that are designed for testing and tasks that are designed for training. In training tasks you are supposed to change your score and these tasks are therefor not ideal for measurement, whereas test tasks should ideally be more robust to change.
There are some clinical tools that have been established for assessing short-term memory. These tasks include Raven's progressive matrices and the Corsi block task. The advantage of these tests is their comparability between individuals. A disadvantage is that they are rarely computerized and less accesible outside the neuropsychological community.
WM is a very broad and colorful concept. Maintaining and updating information are two separate aspects of WM. The first requires sustained attention, the second requires flexibility of thought. Traditionally, the upper limit of the capacity for a number of items is measured. This is equivalent to storage in short-term memory.
However, one further requirement for defining WM is the online manipulation of maintained items. The size of the short-term store - number of items - is just another index of WM performance, although it is still considered the gold standard. However, the score is heavily dependent on what task you choose.
As a student I am currently working on a classical working memory task for testing that runs in your browser. I hope to release it this year as open source. There is still much work to be done to give people at home the ability to test working memory.
Finally, motivation and working memory are strongly linked. Comparing yourself to your peers can reduce performance. It is therefore better to take a "master-oriented" approach and to compare your score with your previous scores.