Hi Kurt. I haven't done a GT262, but it is very similar to others that I have done. This shouldn't be too hard for someone with your experience.
Remove the deck. If the tension spring is the one that's already off, take a good look to see if the belt is still good or needs to be replaced. Maybe the spring broke.
Remove belt guides #23 and #15. You may have to remove the electric clutch on some models to get at #15. If no interference, unplug the PTO wire if it has an electric type, to remove the belt.
Should be able to remove the belt without removing any more belt guides.
Try to shake the tensioner assembly. If it has a lot of slop, the #4 plastic bushings may need to be replaced.
Reverse order for assembly with new belt.
There seems to be a variation as to where #29 spring anchors compared to the models I have done. Hopefully you can spot the worn areas where it attached.
tommyhawk