By plane:
You arrive at Brindisi Airport (35 km from Lecce)(Alitalia schedule). There is a shuttle bus service arriving in Lecce at Piazza Mazzini

By train:
There are direct connections to Rome and to Milan-Bologna (http://www.trenitalia.com/)

By car:
Take toll-highway A14 to Bari; then follow signs to Brindisi-Lecce