How to make single cycle processor pipelined?
If every complete operation takes one cycle, then pipelining using the same cycle time won't give you any advantage whatsoever. 

What you would do is to split up each operation in various parts. First you make the cycle say four times shorter, so now each operation executes in four cycles. Then you split each operation into say five parts, and you have a first stage doing the first part and moving the results to the second stage, then a second stage doing the second part and moving it to the third stage, and so on. It will take all in all a little bit longer because you need the time to move data from one stage to the next. 

And now you have five different stages, you can start pipelining. The first stage does the first part and moves the result to the second stage in the first cycle, and in the second cycle it starts work on the first part of the next instruction and so on.

You win because now the cycle time is four times shorter, so you can do up to four times more operations per second, working on up to five instructions at the same time.