It order to replace the back, it must be pressed or "snapped" on.  Sometimes this can be done with just your fingers, but more often than not a tool must be employed to do the job.  Case closing pliers can be used, but they can put unnecessary pressure on the crystal that may crack it and cost much more that the money saved by buying a less expensive tool.  Take great care.  Though not Swiss precision, a nylon case press protects the crystal and will be less likely to scratch a watch.  You can also find economy nylon case closers here and here.  A case closer with metal dies will give a firm, even press, but care must be taken not to scratch the back of the watch.

If you are looking for top quality Swiss case presses look to the Horotec Mini Press, the Horotec Standard Press or the Horotec Deluxe Press
 

When replacing the back, a new waterproof gasket should be installed to properly protect the watch.  Most manufacturers will not honor a warranty if a professional does not perform the work.