I worked at my computer last night. I think this is the clearest.
I worked with my computer last night. This is still pretty clear.
I worked on my computer last night. This is clear only in context because the reader listener can parse the sentence two ways:
- I [worked on] my computer. --I repaired it.
- I worked [on my computer]. --I used my computer to do some work
Realistically though, these phrases all work and will rarely be misunderstood. I would say "I did some work on my computer last night," and that has the same ambiguity as the third sentence above. Sometimes you just rely on your reader/listener to have some common sense ("What do I look like, a hacker?"), but it doesn't always work.
Student or Learner