Yes, it is possible by train or by bus.
Train timetable : www.trenitalia.it
Bus timetable : http://www.aziendasicilianatrasporti.it/

Azienda reads;; paginaoria not found
Google says that all we know so i,ll
revisit as system may be down.
As for Trenitalia 2 morning dep.
from Modica 5.44/6.10 or 11.53/12.18
Coming back an evening one 7.04/7.23
Would the one getting in around midday
be sufficient then catch the 7.04pm back

Back again with better news as persistance
pays !!!!
Busses to Ragusa 4 a day
5am...8am...1pm..& 5pm
Returning to Modica 4 a day
7.30am...11.45am...2.45pm..& 7pm
Thanks for your input and this
may assist others

Make sure you double check the schedules on the ground when you are there -- never get off a bus and wander away without looking at the posted schedule to make sure you know when that return bus leaves according to the posted schedule.

Also, make sure you know which days might be holiday "festivi" on your travel days. Sunday is always a "festivi" schedule, but if you are traveling around Easter or April 25 -- just check with whomever is standing nearby.

Just in case you don't know this already: remember that you have to validate your tickets when boarding the bus (stamp them in a little machine - watch how other do it). Inspectors sometimes board the bus to check that all the passengers have validated their tickets. If your ticket has not been validated (and hence could be re-used), you can be fined.

Yes i heard about the validation thing and
will be vigilant
Also i am traveling Wed and Thursday and will
be diligent with bus timetables and their posting
Also pay particular attention to where i get
dropped off.
Three months on public transport in Africa
taught me to check,check & check again
Am getting realy excited about Sicily
Thanks everybody you have smoothed it a lot

Beware that what you are reading now are the winter timetables.
They might change in spring/summer.