The recumbent cycle is a good exercise for working both the heart and lungs and also the Gluts (buttock) muscles and hamstrings. With the high seat position this is a good exercise for those persons who suffer with back problems.
Most recumbent bike models come with handles either to the front or side, either of which will give a comfortable ride.
As with any cycle machine, adjust the seat to allow your legs to rotate smoothly, with ideally a 15 degree bend at the knee joint. Excess stretching or sitting in a cramped position, will tire your muscles.
Try and avoid pushing down on your legs with your hands, let your legs do the work.
If cycling for more than 10 minutes, aim to have a water bottle and towel with you, so you can stay hydrated and wipe any sweat away from your face.
Throughout the cycle, look at keeping a minimal movement from your upper body, some people will have a tendency to bring their shoulders forward, in an alternate leg action.
Aim to build up the resistance and distance / time you spend on the bike over a gradual period, with the first few minutes used to help with warming up your leg muscles, always remembering to stretch both before and after your session.