Mysore Palace is open for visitors on all the days. In other words there is no weekly off for the palace.

There are two themes as far as visiting the palace is concerned. During the day time visitors are allowed to visit the palace building. That is museum inside of the palace.

In the evening visitors throng the palace area to see it under the floodlight .
On the weekend ( Sundays 7 PM to 8 PM ) what appears to be a million lamps ( 97,000 bulbs, to be precise! ) silhouetting the palace is switched on. Also on national holidays and state festivals this special illumination is kept on from 7 PM to 8 PM. During Dasara festival season this illumination is kept on on a daily basis and also for longer duration (see Mysore Palace illumination).

Visiting hours for the palace museum is from 10 AM to 5.30 PM. Ticket counter is adjacent to the entry point. That is the south gate. The parking area too are located near this gate.

Camera is not allowed inside the palace buildings. Mobile phones need to be switched off. However you can take photograph the palace from within the palace campus. There is a camera locker facility within the compound. This kiosk appears on your right after you buy the entry ticket and enter through the gate into the palace campus. Rate is Rs5 per camera. They lock the camera and give you the vault key along with the coupon. See to that you collect back the camera before 5.30 PM.

From here it's a 5 minutes walk to the palace proper. If you need guides, hire on this way. As you enter the palace building you've to leave your footwear at the shoe counter and collect the coupon.
Beyond is the place where they ask for the entry ticket. In the immediate vicinity is the kiosk where the audio tour gadget can be hired. Audio tour is available in Kannada, Hindi, English, French, German, Italian, Spanish and Japanese languages. At strategic points audio tour signboards are placed with specific serial numbers displayed on it.

You need to play that number in your audio tour player, where you listen narration highlighting the corresponding landmark/object.
The audio tour gadget is similar to a walkman or a ipod with a headphone. Fee for the audio tour is Rs100 ( Indian nationals) / Rs200 ( foreign visitors).
There's no time limit on how long you can take for the tour. The only limitation is the opening and closing visiting hours.

Beyond the first palace tour is the second palace. This is the residential palace, much smaller and more human in scale. This houses the Residential Museum. You've to buy ticket again for the residential museum tour. The ticket counter is on the way to the residential palace.
After this you can pick your footwear from the shoe stand and collect camera , if you have it deposited with the locker. Now you are free to tour the palace campus.

See also Architecture of Mysore Palace and Photography in Mysore Palace
Other attractions inside the palace compound include the many temples within the palace, (see Temples in Mysore Palace) the open gallery where many ancient artefacts are on display, the silk showroom , the garden and the souvenir shop. Of course there is small elephant and camel safari option too if you are game for it.