There are several ways to do this, depending on exactly what kind of application you have.
If you're making something interactive, you can take a user to the submit page with a URL and title already filled in. The following URL will open the reddit submit form with a link to this question:
http://www.reddit.com/submit?url=https://stackoverflow.com/questions/24823114/post-to-reddit-via-url&title=Post%20to%20Reddit%20via%20URL
If you just want people to be able to submit your site or blog post to reddit, you can use a reddit button on your page instead.
If you're writing an app or a script where you need to post a URL to reddit, you can use the /api/submit route in the reddit API. If the user that is submitting the link has less than 2 link karma, then a CAPTCHA will probably be given.