Churchill flew to Moscow in 1942 to inform Stalin that there wouldn't be a second front that year. The other plan having his cabinet colleagues was stuck in Teheran, which prompted the question in the first place, what route did Churchill's plane take? What aircraft did he travel in?
Likewise, similar questions about the conferences Roosevelt attended.
What kind of fighter escort was provided? How did the three nations go about securing the actual conference venues?
There are a few similar questions in the archives that might be of interest, I'll draw on some of my previous comments (particularly from the first) to concentrate on Churchill's travels:
For the 1942 journey to Moscow, stopping off in North Africa for a week or so, the aircraft Churchill flew in was a modified B-24 Liberator [named "Commando"] (http://www.iwm.org.uk/collections/item/object/205189669), subject of [an article on the Smithsonian website] (http://www.airspacemag.com/history-of-flight/travels-with-churchill-136166507/?all). The long range of the B-24 was important, as the usual route for Allied aircraft to the North African theatre (and the original route proposed for Churchill) started from Takoradi in Ghana (the Gold Coast, as was) and took five or six days travelling across central Africa before heading north to Cairo (as illustrated on [this map] (http://www.ibiblio.org/hyperwar/AAF/I/maps/AAF-I-10.jpg)). The B-24 could fly directly from Gibraltar to Cairo.
The first leg of the journey was Lyneham to Gibraltar, arriving the morning August 3rd, which Churchill describes as uneventful in The Hinge of Fate. That evening they took off at 6pm, cutting across Spanish and Vichy territory with an escort of four Beaufighters, flying across North Africa largely in darkness, seeing "in the pale, glimmering dawn the endless winding silver ribbon of the Nile" (ibid) on the morning of August 4th. Churchill visited the Alamein positions on the 5th, and appointed General Gott to command the Eighth Army. On August 10th Churchill departed Cairo for Tehran, then on to Moscow, arriving on the 12th. The conference lasted until the 17th, the return journey followed the same route in reverse, again including some time on the desert front.
In general there was little risk of coincidental interception for aircraft avoiding combat zones, especially at night; integrated air defences, radar and night fighters were concentrated in the UK and Germany, and to a lesser extent other active theatres. Air travel always carried an element of risk, though; on August 7th the newly appointed Gott was flying in to Cairo, on a similar route to the one taken by Churchill on the 5th, when his aircraft was shot down and strafed on the ground, killing most of the passengers (somewhat ironic, given Gott's nickname of "Strafer"); this resulted in Montgomery being appointed to command the Eighth Army. Knowledge of exact routes was limited as far as possible to the aircrew themselves, as intelligence leaks were a risk (e.g. Yamamoto's aircraft was shot down in 1943 by USAAF P-38s acting on "Magic" intelligence). Also in 1943 a BOAC DC-3 airliner was shot down as it flew from Lisbon to Britain, one of the passengers was the actor Leslie Howard; there are [numerous theories] (http://www.defensemedianetwork.com/stories/the-shoot-down-of-leslie-howard/) that the aircraft may have been deliberated targeted in the belief that Churchill was on board, or that Howard himself was the target due to his work with British Intelligence, or that it was merely a mistake. Air accidents were probably the main danger, numerous high ranking officers were lost in air crashes (e.g. Air Chief Marshal Trafford Leigh-Mallory, Lieutenant General Frank Andrews, Major-General Orde Wingate etc.)
Churchill continued to use "Commando" until 1943, when it was replaced by an Avro York (a design derived from the Lancaster) named "Ascalon" with a few more creature comforts including a heated lavatory seat (though apparently it was disconnected as it was too hot), then in 1944 he switched to a C-54B Skymaster received via lend-lease; an article [in Flight magazine from November 1945] (https://www.flightglobal.com/pdfarchive/view/1945/1945%20-%202348.html) outlines how it was fitted out with rather luxurious passenger compartments, a conference room (with cocktail cabinet) and a well-furnished galley.
