Hi Diane, First you'll need to decide how large a bed you want and can handle. Draw out a design for yourself with the possible measurements and then you can use recycled lumber etc to build one to suit your needs.
Here's one already done so you can see some of the issues you'll need to consider.
Hope it is helpful to you. https://www.youtube.com/watch?v=rjKbgeXijiU
here are ideas/videos https://www.youtube.com/results?search_query=diy+raised+garden+beds+on+wheels
Make sure it is of a size that you will be able to move with the weight of the raised bed, moisture, soil and plants. It could get heavy real quick. If need be, build more than one to accommodate the plants you want to grow.
We mounted wheels onto a pallet and then screwed a broken plastic baby pool to go the pallet. We added rope handles to opposite sides. Then we took a tomato cage and bent the bottom legs with pliers so we could connect them the center of pool with heavy duty zipties screwed to bottom through to the pallet. Drilled a few more drainage holes along the outside bottom edge. Filled it with our dirt. Planted what we had chosen. Placed it on our front driveway and moved it from side to side chasing the sun. It worked great and was easy to water. But we left it behind when we moved.