Assessment of, as, and for learning are not specific methods of assessment. Rather, they can be considered categories of assessment. Sometimes they are reduced to synonyms for summative and formative assessment, but that is an oversimplification. In reality, they describe different approaches to assessment that all work together to reinforce the learning process.
Assessment of learning.
The most classic example of assessment of learning is the summative assessment. This approach to assessment is typically formal and is often what determines grades. While it may be considered the most objective form of assessment it also fails to account for the unique circumstances of the individual students.
Assessment as learning.
Assessment as learning is sometimes argued as the most important of the three categories. The classic examples of assessment as learning are self-reflection and peer assessment. In this circumstance, the responsibility for assessment is typically given to the learners who then use it to self-adjust and learn from their mistakes and successes.
Assessment for learning.
The typical example given as assessment for learning is formative assessment. In this model assessment is ongoing and results, not in grades or concrete measurements, but in continuous specific adjustments.