The first thing you do is look to see if something has worked loose and needs to be adjusted and tightened. So that's making sure the crank arms aren't loose on the BB axle, and making sure the BB bearings haven't just worked loose.
The axles themselves rarely wear to any significant degree; any slackness will almost always be a bearing problem. If it's a traditional adjustable type it just needs lubricating and adjusting with possible ball bearing replacement. If it's modern sealed unit junk engineering type the whole BB unit will need to be replaced.