Ostend-Bruges International Airport is slowly expanding into regular passenger service. However, most flights are still charters, so your best bet is to fly to Brussels and drive or take the train from there.
Considering the flat-as-a-pancake terrain, it's easy to travel on two wheels. You can rent bikes at rental shops or at the ticket windows of train stations. A valid train ticket gets you a discounted rate. Many bike rental companies have both adult bikes (with or without baby seats) and children's bikes. Maps with suggested cycling routes are available at local tourist offices.
The De Lijn bus company provides bus, tram, and trolley service throughout Flanders. Roads in this region are well maintained, with good signage. Be sure to watch out for cyclists.
To visit the battlefields from here, driving is definitely the best solution, because the various World War I sights are in different directions from Ieper. The easiest way to reach Ieper is via the A19 from Kortrijk, which peters out north of the city; highway N38 continues to Poperinge, where you're close to the French highway linking Lille with Dunkirk and Calais.
The Belgian national railway, NMBS/SNCB sends two trains each hour to Brugge from Brussels (50 minutes) and three trains an hour from Gent (25 minutes) and from Oostende (15 minutes). Oostende is the terminus of the Cologne-Brussels-Oostende railway line, which connects with the ferry service to Ramsgate and the boat train to London. A train departs every hour from Brussels (1 hour, 10 minutes), from Gent (40 minutes), and from Brugge (15 minutes).