Circumstances varied considerably depending on nationality, location etc.; presuming he was a pilot in Bomber Command based in the UK 20 sorties might not seem like much over years of war, but the training period was lengthy - up to two years for bomber pilots. Presuming no flight experience they would start from scratch with lectures and classroom training along with drill and the like, then first take to the air in a simple biplane like a Tiger Moth (many pilots receiving flying training in Canada, with better weather and no risk of enemy intervention). Flying then progressed with more complex multi-engine aircraft like the Oxford or Anson. With Elementary and Advanced training complete the pilot would move on to an Operational Training Unit (OTU), equipped with the aircraft they would actually fly in combat, for two to three months before before posted to an active squadron for their first operational sortie. Good old military bureaucracy could easily extend matters as pilots trekked around trying to find the units they were assigned to, who might or might not be aware of their impending arrival.

For active squadrons flying depended heavily on the weather. The 20 missions were (presumably) operational sorties, but he likely flew more often. Heavy cloud or fog over Britain or the target would cause missions to be scrubbed with varying levels of notice; crew could be briefed and ready then stood down, or even in the air on the way to the target before being recalled, flights that would not count as operational sorties and not be recorded as such. Technical trouble with an aircraft might also cause an early return, again not counting as an operational sortie.

Between missions there was a variety of day-to-day activities - test flights, lectures, etc. If crew were stood down it depended on the individual; quieter types might read a book, write to friends or family or just catch up on sleep; more extroverted types were more likely to head for the mess on base or a local pub, if one was close enough. Films, plays or variety shows put on by the likes of the ENSA (the Entertainments National Service Association, though the variable quality led to a variety of other suggestions like Every Night Something Awful) were popular, either on base or in local towns, and dances, particularly those with WAAFs or local girls. Longer spells of leave could be spent with friends or family, or London was a popular destination, especially for overseas crews.

There's a superb website with the diary of Bruce Johnston, a Canadian Lancaster pilot; Johnston kept a marvellously detailed diary, and the entries have glossaries of the RAF jargon used. Though he joined the air force in 1942 his first operational mission was in June 1944, his operational tour of 30 missions completed in September of that year. Flipping through the August 1944 entries, for example, he flew 11 missions that month; between them he met friends, wrote a lot of letters, watched several films (including 39 Steps - "Good", Hit Parade of 1943 - "wasn't at all bad", This is the Army - "average"), collected a motorbike (despite never having ridden one before), and was unimpressed by Alfredo's Band ("rather poor I thought" on the 22nd, and hadn't improved on the 23rd when "it stunk!").

Another transcribed diary is in the collection of the International Bomber Command Centre, that of Hedley Madgett who was shot down in 1943. He was a less prolific diarist than Johnston, only recording sortie details once at an active squadron, but it's still a fascinating document (as is the 1942 diary covering training).

More generally Kevin Bishop's three books, Bomber Boys, Men of Air, and Journey's End, are very good (broadly covering Bomber Command in 1943, 1944, and 1945 respectively). They're based heavily on personal testimonies and mostly focused on the flying, but also cover aircrew life in general.

Follow up. What did crew do after they'd flown their 20 missions? (should they be lucky enough to survive)