Just on the off chance that this isn't a troll/wind up.
You just use allen keys and spanners (sized appropriately), and then check for play.
You'll need to buy a bearing/bush kit – try betd.co.uk
If there is play, the bearings/bushes are all push fit, so no specific tools needed.
Most likely:
1. Reducer bushes on the shock eyes
2. seat stay end of rocker (bush)
3. chain/seat stay bush
If this isn't fairly obvious without having to ask, you may be better going to your bike shop.
If anyone knows where to source individual bushes, to avoid buying a full kit, that would be useful.