If you're using a third-person omniscient narrator, just start a new paragraph, and use framing text to let the reader know the scene is changing:

Sally didn't know what was going to happen to her next. Who was this mysterious man who'd been holding her captive? She finally let herself cry when the door closed and she was once again alone in the darkness.

Upstairs, Jim took off his mask and thought about all his delicious plans for his new toy. He really hoped that This One would last longer than The Others.

If the first part was being told in first person, you could keep the same characterization of your narrator, but give her more information as a narrator than she had within the story, to sort of turn her into a third-person omniscient with respect to the other character. Something like:

I didn't realize it, but over on the other side of town Jerry Watson was working on a project that would prove to have serious consequences for me. His mind was wandering as he mixed the chemicals, thinking more about the blonde he'd danced with the night before. He wondered if she'd be back at the club again that night.

If you want to tell both pieces in first person, you could be blunt and insert the character name before their piece. If you shift back and forth frequently, you could make it read like the transcript of a double interview.

Emily: I saw this guy walking into the store, and he seemed kind of nervous. I know it's silly in retrospect, but I was kind of afraid he was going to try to rob the place.

Steve: I definitely was nervous. I felt like I'd been sweating through every layer I was wearing, and I was sure that the cute shopgirl knew what I was there to buy. I very nearly panicked and ran out of the place, but I'd already come so far.

If you're going to start with one narrator, go for a long bit with a second narrator, and then switch back to the original, another way of going about it would be to change the style, color, or typeface of the text for each narrator. This is especially useful, if you want to keep the identity of one of your narrators secret.

It had felt so liberating! I'd spent the day in a dress and no one had seemed to notice at all. My worries had been for nothing. I changed into my prettiest nightgown and slipped into bed.

It just wasn't right that a freak like that was allowed out in public. I wasn't going to let my hometown turn into a place full of perverts. Something had to be done, and it seemed like I was the one who'd have to do it.