Hyderabad is connected with Mysore by road, rail and air. The road distance between Hyderabad and Mysore is about 700 km.

Road Route: The road is essentially NH7 from Hyderabad all the way up to Bangalore (some 560km) and then the sate highway (SH17) between Bangalore and Mysore, which is about 140 km.

Broadly the route is Hyderabad -> Mahabubnagar -> Kurnool -> Anantpur -> Penukonda -> Bangalore-> Mysore.
Your drive will be more or less smooth along the fast moving traffic except the lap of crossing Bangalore city.

There are various competing theories on how to skip the traffic bottlenecks of Bangalore city. Many times these strategies keep changing depending on the perpetual road developments in Bangalore.

One of the options, though a bit longer, is to bypass Bangalore city along its northwestern periphery till you hit the Mysore road.

So bypass route is like this. Some 35km from Bangalore city, the NH7 crosses Devanahalli where the Bangalore  International Airport (BIAL) is located. At Devanahalli ( before the airport ) leave NH7 and take the right turn towards Dodballapur. Now you are on NH207. At Dodballapur ask for the direction to Nelamangala. At Nelamangala turn right into the NH4 (Tumkur road) towards Bangalore. Ahead on this road, you'll hit the NICE Road (express way with toll booth). Take the road that indicates direction to Mysore. You'll finally hit the Mysore Road (SH17) at the southwest outskirts of Bangalore city. From here it's about 2½ hours drive to Mysore. ( See also Bangalore to Mysore road map)

Bus :

KSRTC operates two direct bus services (A/C Volvo ) from Hyderabad to Mysore via Bangalore. If that is not feasible, look for one of the many bus services between Bangalore and Hyderabad. There are both private and KSRTC/APSRTC services. Further from Bangalore to Mysore you have many options, all typically takes about 3 hours of travel.

Trains :

There is only one direct train from Hyderabad to Mysore, the  biweekly Jaipur Mysore Express ( Train No: 12976 , for return Train No 12976). If that is not feasible, a practical option is to travel to Bangalore and look for a road or rail connection for the onward journey from Bangalore to Mysore.

There are 3 daily trains from Hyderabad to Bangalore , and many weekly/biweekly trains that connect Bangalore and Hyderabad.

The two most convenient trains daily trains are the Kacheguda - Yesvantpur Express ( Train No: 17603) and the Bangalore Express ( Train No: 12785), both starts from Kacheguda (KCG) station. The first train ends at Yesvantpur Jn while the later goes all the way to  Bangalore City Junction. Yesvantpur is some 10km from Bangalore city station. For the return journey to Hyderabad, the train numbers are 17604 and 12786 respectively. Both pairs are overnight trains that takes about 12 hours.

Even the Rajdhani Express (Train No.12493/12429 & Train No.12494/12430) connecting Bangalore with Delhi passes via Secunderabad Junction.
Some of the trains connect Bangalore with Hyderabad are : Wainganga Exp (Train No. 12252 , via Kacheguda ) ; Kongu Express ( Train No. 12648) via Kacheguda ; Gorakhpur-Yesvantpur Express (Train No: 15015) via  Secunderabad Jn ; Karnataka Sampark Kranti Express ( Train No 12650) via Kacheguda .

Flights:
Though Mysore has an airport there are no direct flights to Mysore from Hyderabad. Take one of the Bangalore flights in the morning and there is a Kingfisher connection flight from Bangalore to Mysore. ( See also Chennai to Mysore by flight)