Take the bus - very inexpensive - catch it on the Promenade - or at the bus station - very easy...! Note: if you are waiting for the bus and the number you want to take is approaching - you must step out and wave for it to stop at the bus stop - it will not do so automatically...

The best option is to go by rail. SNCF, the French rail network, operates a line that connects all three places. It's about 40 minutes between Cannes and Nice; 20 minutes from Nice to Monaco/Monte Carlo. If you're thinking of dotting around France and other European countries, you might want to consider a multiday rail pass.