Certified GKH Gardening Expert
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Generally, your container size will depend on the size of your palm at the time. Roots should fill out the container, and there should not be more than 2 inches of uncolonized soil between the root ball and the container at any time. This will be to avoid root rot, ultimately.
Once your current container's root ball is able to be pulled out in one piece, you can place it into a container that is no larger than 2 inches larger on all sides.
Place 2 inches of soil on the bottom, then place your palm. Fill in the soil all around and about 2 inches on top of the original soil level. Once you water in, this will settle out some. If there are any gaps, then repeat.
Make sure your container has drainage holes to allow all extra water out into a saucer that can be removed from under your plant. That way you can remove all extra water after about half an hour to avoid root rot.
Only water once the soil is bone dry down to about 1/3 of the way into the container.
Generally, if you repot every year, then fertilizer will be unnecessary. If you wait every two years, then you can fertilize with an all purpose granular once during the second year.