Light the scene with professional lighting. Use key and fill lights, as well as back lights. Be sure not to drown your scene with light. Usually, a camera sees less light than your eye, so if you use no light, most shots will appear dark, especially indoors.
Make sure not to overexpose the camera. White, for example, is not usually plain white, but might be a mixture of grays and whites. If your film shows white as pure white, it's a dead giveaway that it's video. Turn down the lights some and you may be better to add brightness in editing. Be sure to use the white balance function for the appropriate setting.
Set your camera to shoot 24fps because this is the speed 35mm film usually plays at. Make sure you set your camera's settings to manual and adjust for each shot. Using the auto mode will make everything look the same and less like 35mm. Zooming in from far away may also helps to provide depth of field. Additionally in editing, using a rack focus effect can add depth of field.
Shoot in wide-screen using some type of high-definition video. Films are not shot in the standard 4:3 aspect ratio, unless it's for TV. Wide-screen will give the film a very cinematic look. If your camera can work with a 35mm adapter, you can use a 35mm lens, and that will also significantly help.