Tours to Escorial

There is the more or less hourly suburban (cercania) service #3 from Atocha, Sol and Charmartin stations to El Escorial (schedule on: www.redtransporte.com/madrid/cercanias-renfe/horarios.html). From the Escorial station it's a short walk to the palace cum monastery.
For Segovia the bus looks the best option for its frequent departures: www.lasepulvedana.es/rutas-horarios.php The Moncloa bus station is served by the metro.

^^ I would say it is the opposite. The bus is most convenient to visit El Escorial. The bus station is a short, few block walk from the palace while the train station is quite a distance and not really that walkable. Buses leave frequently (about every 15-20 minutes) from the Moncloa station in Madrid.

For Segovia, the AVE train is convenient from Chamartin station and much faster and there are local buses from the station that take you right into the plaza at the aqueduct.

I have not taken organized tours of either and can't recommend one.

Both El Escorial and Segovia are great daytrips from Madrid and easily doable on your own. My kids and I took a bus out to El Escorial and it was just fine. As said above, the bus drops off not too far from the monastery. An easy walk. Bus travel in Spain is comfortable.