When taking pictures of strangers you should always ask permission, if you plan to use it for resale or print, you want to get signed documentation that this person is letting you use their photo. If it's for a personal project that isn't public, it's fine to just ask for permission.
Photos that you plan to label as photojournalism and editorial pieces don't always need to have a signed contract between you and the model/subject, but it's always good to cover yourself just in case.
When you ask someone if you can take there photo, be confident. Try not to dance around the subject. Have a clear outline of what you are going to say before you say it. Confident people come out much less suspicious than someone mumbling and stuttering as they explain why they want to take pictures of a random stranger.
Many people are happy to let you take a few shots. Remember not to push it. You just met this person, don't make them feel uncomfortable by holding down your shutter and snapping off a hundred photos or dictating poses. Even street performers, public figures and celebrities can be taken off guard by an over snappy photographer.
Now let's say that you plan to use a photo in a commercial piece, or in your gallery for resale. You need a model release. Here's a site with more information about when you need one and when you don't:
Here are a few sites that have some basic templates, and examples of model release forms. Read them! Don't just slap your name on it and go without reading it.