It rather depends on the individual and location. They may have been injured, either from whatever caused them to bail out in the first place or the jump itself, in which case handing themselves in would usually be the sensible action. If deep inside uncontested enemy territory then their chances of evading capture were extremely slim; German aircrew over Britain, for example, faced a populace at a high state of alert (especially during the invasion scare of 1940), and the prospect of having to get off an island; the longest recorded case of a German airman on the run was Josef Mezl who, for nine days at the beginning of August 1940, remained hidden in woods around Newbury after bailing out of his Heinkel 111 at night. Finally, realising the futility of his situation, he decided to give himself up and headed to a road where he encountered the car of Lady Buckland. She instructed her chauffeur to collect Markl and proceed to Newbury police station, where she demanded the arresting officer give him a good meal. The other four members of Markl's crew were more typical; two elected to give themselves up immediately, the other two were found within 48 hours by Canadian troops called in to search the area. One pilot, Franz von Werra, did make it back to Germany - via Canada. Many German PoWs were taken overseas, von Werra escaped from a train on his way to a Canadian prison camp and got to the (then neutral) United States.

Likewise Allied aircrew over Germany faced a hostile populace, particularly later in the war as the combined bombing offensive dramatically increased in scale, up to 1,500 being killed by lynching or mob violence. Few evaded capture, and though there were escapes from prison camps (as popularised by e.g. The Great Escape) less than 30 RAF personnel reached Britain or neutral territory after being captured.

The best chance for Allied aircrew was if they landed in occupied territory (e.g. France, Belgium, The Netherlands), where a number of Escape Lines operated, assisting escapers and evaders (often aircrew), at enormous personal risk. RAF aircrew were given instruction on escape and evasion, and issued with an "Aids Box" containing "compressed food, Chewing Gum, Halazone, Benzadrine, Matches, Safety Razor and Soap, Needle and Thread, Surgical Tape, Fishing Line and Hook, Water Bottle and small compass". The kits were issued by MI9 along with silk maps, purses containing foreign currency, and more than two million compasses of various designs including ones designed to be hidden in buttons or boot heels. The aim was "to give the evader sufficient nourishment for 48 hours and so enable him to lie up or move from his original location without the necessity of obtaining food", with the maps then offering the chance to find a town where help could be sought. MI9 reported that 4,657 British Commonwealth personnel evaded capture over the war.

The USAAF also issued various kits as detailed by /u/the_howling_cow in a post from a while back. Aircrew who escaped or evaded capture were thoroughly debriefed when they returned to friendly territory with the results written up in an Escape and Evasion Report, almost 3,000 of these reports from the 8th and 9th Air Forces have been digitised and made available by the US National Archives. Some of the lessons learnt were distributed in a booklet during the war, reproduced on the website of the Air Forces Escape & Evasion Society. For example, shaving might not seem like a high priority when on the run but according to Lt. Col. Lay: "All Americans should shave frequently when in France because the Frenchmen are clean shaven and if you have a beard you look like a tramp. Some of the older aids boxes do not have a razor. The new aids boxes have a 'Valet' razor with only one blade and the single edge razor is hard to get, so take along another razor with an extra package of blades."

Over the course of the war, there were some extraordinary cases. Sergeant Bob Merlin of 175 Squadron was shot down over France in August 1943; he managed to make contact with the local Resistance and, being fluent in French, assisted them in gathering intelligence on the V1 launch sites being built in the area, acting as driver for a civilian sub-contractor. He even met the crew of the flak battery who shot him down in a café on his travels! He took the information to Switzerland in November 1943, where he was interned, passing it to the British Air Attaché; getting bored of skiing he then escaped again, back to France, in spring 1944, and joined up with the Resistance again as they assisted with the Allied invasion. In September 1944 175 Squadron were based at Vitry, and were somewhat surprised when a mysterious bearded figure arrived, driving a German Kubelwagen with an Alsatian in the back. It was Merlin, who subsequently re-joined the squadron, only to be shot down again on Christmas Day 1944 during the Battle of the Bulge, fortuitously surviving again to see out the war.