Toledo's old city is entirely walkable — in fact, the only way to see most of it properly is on foot. The streets are narrow, steep, and cobbled, and no vehicle larger than a small motorbike fits through many of them. Comfortable shoes matter.
The tourist train (Trainvision) runs a 45-minute circuit from Plaza de Zocodover, stopping at the Mirador del Valle viewpoint and a few other points. It is useful for the panoramic view and for visitors with limited mobility, but it covers less ground than a morning's walk.
Taxis are available but can only access the edges of the old city. Most visitors arrive by bus or car and park outside the walls. The bus station is about a ten-minute walk from Zocodover. From Madrid, buses run every thirty minutes from the Estación Sur and take about an hour.
The city can be done comfortably as a day trip from Madrid — the early bus, a full day, and the last bus back. But Toledo rewards an overnight stay. The city empties in the late afternoon when the day-trippers leave, and the streets in the early evening have an entirely different character.