Personally, I like to use italki to find language exchange partners. By clicking on the "Community" tab and choosing "Language Partners", you can search for people who speak the language you want to learn and are hoping to learn or practice the language you speak. You can also choose if you want them to be male or female, specify a city (if, let's say, you hoped to meet up some day - or if you're looking for someone in your time zone), and decide whether they need to be a native speaker or not. From there, click on profiles that look promising and add friends! Once your friend request is accepted (or you accept theirs) you can use the messaging system to chat back and forth a little and decide if you want to be language exchange partners. Side note: I really dislike the messaging system on here. It seems better than when I started but it's still not great.

After getting to know them I suggest adding them on Skype (only do this once you're sure you're comfortable with them!) and then deciding how you want to teach each other or practice. This can be tricky if you're at different levels with your languages, which has usually been the case for me. If your partner is pretty good at your language and you're just a beginner at theirs, don't get discouraged or feel embarassed. It's tempting to let them keep practicing your language at that point because you don't want to switch to theirs - it's harder for you than speaking your own language AND you're feeling embarassed/discouraged! If you let them keep practicing, they probably will, and then it stops being a partnership and it starts being a private practice for them. While it can be beneficial for lots of reasons to chat with someone from another place, if that's not what you're here for then you're wasting your time.

If you're a VERY beginner at the language (especially if you know they're quite good at yours and could reasonably answer some questions), create a list of questions you have about the language. How do you say "(basic phrase)"? How do you pronounce this letter that doesn't exist in English? Stuff like that. It also really helps to know how to say things like "Please speak more slowly" and "Please repeat that" or "Can you type that out/write that down" in your partner's language.