There are about 20 spaces along the road at the Toxside School end.... It is a 10 minute (half a mile) walk from there to the swim spot opposite the main island. (see walking route below)

.....also there are 2 spaces for cars on the layby on the west side (towards Moorfoot farm) -- you'll need to walk along the path through the woods to get to the swim spots - Google Maps Location. You'll see wild hare and deer and plenty of birds going this route. From there it is a 20min walk (1 mile) to the northern side - opposite main island.

Skinny Dipping Spot:

If it is not busy then you can Skinny Dip on the northern side (opposite main island). Else walk along the west side towards Moorfoot farm where no-one typically ventures. Gladhouse Reservoir has a very shallow bank and so you can end up walking for 20m before you even get below waist line! 

Best Time To Go:

I recommended going first thing in the morning on days when it is not too windy. The sunrises are amazing.. (though they take 15 - 20 minutes to rise above the Moorfoot Hills after the official sunrise time)
It is a perfect location for evening camp fires and moon or star lit evening dips -- though fires must be on the rocky shoreline and not the bank. 
The nearest weather station is Gorebridge - Check the MetOffice.

Safety:

Just be aware that Gladhouse Reservoir has lots of large loose rocks on the shore. You might need to wear swim shoes to protect your feet. The small island is home to wild birds and so you mustn't land on it. You can swim over to the main island but aren't permitted to venture on to it. Watch out for fishermen in boats -- but the water is so huge that they tend to stay well clear of the busy swimming areas. If swimming at night remember to place some lamps on the bank so you know where to swim back to. Mobile phone signals are vary patchy in this area too. 
Also, be aware that there can be lots of algae during the hot summer months.... it can be fatal to dogs and can cause illness in humans so best avoiding the place if you notice any. When the water temperature is above 19c there is a chance of being infected with Duck Mites. You will feel very itchy and will need to shower.... Antihistamines and Chamomile Lotion will required for at least 3 days until they die. If you itch the contaminated areas on your body make sure you use antiseptic gel/wash to prevent infection. 

Recommended Links:

Edinburgh Skinny Dipping Stories facebook group

Glamourous Gladhouse Swimmers facebook group

Photographs

Cheeky Skinny Dipping Photos