Summary: Some ideas for using language exchange sites
A conversation exchange is when two people who want to learn each others' languages swap lessons, for example spending half the time together speaking English and the other half speaking Spanish. Nowadays, this can also be done online through Skype, and there are sites which specialise in matching up conversation partners. This is usually free and much more fun and relaxed than a proper lesson. As the name "conversation exchange" suggests, however, it is often more like a chat than a lesson. This is understandable when neither of the two people are language teachers and both are shy about asking their (unpaid) partner boring and complicated grammar questions, but there are plenty of ways of learning together that are better than talking about your weekend yet again. Here are some ideas:
Policies and principles
I wouldn't do this the first time you meet, but if either of you feel that you could get more out of your time together it is worth talking about how that could be done. In fact, you could even draw up a sort of contract or list of things you will do every time you meet. This process of drawing up a policy would also be good speaking and writing practice. Things you could decide on include: how the time will be divided up (e.g. ten minutes' chitchat, then five minutes helping with your homework, etc), how often and how you will correct each other, if you will bring in materials for the other person to use, the use of translation (or not), and if the use of the languages will be mixed up or divided up.
Talking about what you think the best ways of learning a language are can also make an interesting conversation, and you could learn more about where your partner is coming from and maybe pick up some useful language learning tips.
Something else you could prepare to help you get the most out of your future studies together is a sheet of paper on which to put all the things you learn during your conversation exchange. For example, you could have one A4 sheet divided into sections for Grammar, Vocabulary and Pronunciation. Another way is to divide it into sections for Corrections, Better Ways of Saying Something, and Other Useful Language. Usually the person whose language is being spoken has this piece of paper and jots down things that they notice or think of during the conversation, to be discussed during a break in the conversation or towards the end of the period speaking that language. It is then given to the person who is studying that language to take home and use for revision.
Read and discuss
Read an article or part of a book before you meet and then summarize its contents for your conversation exchange partner and give your opinions on it. Your partner can ask questions about the content and your views, and then talk about their own knowledge of the topic. It is best if it is a topic they are likely to know more than you about, e.g. something about their country. Otherwise, you might want to let them know what you are going to read or its topic so that they can do the same to prepare something to say.
You could of course do the same thing with videos or radio programmes.
Read up and discuss
Choose a topic on which there are lots of sources in both languages, and perhaps different opinions too. For example, if you are learning Spanish and your partner is learning English, you could choose the topics of Gibraltar or the Falklands/ Malvinas. Both of you should read up on the topic as much as you can in both languages and then discuss the different views and information in the sources, why they might be different, and which views you most agree with.
This is similar to the ideas above, but without necessarily reading up first and with the onus on the person speaking. Choose one topic, e.g. "my family" or "problems in this city", and prepare to talk about it for at least one or two minutes the next time you meet. Preparation could include brainstorming ideas, looking up useful words in a dictionary, writing notes, or even writing out the whole thing (although you shouldn't actually read from what you have written while you are speaking). After listening to your presentation, your partner could ask you questions, correct some mistakes, tell you more complex ways of expressing yourself, or just talk about the same topic themselves.
I found this to be by far the most useful thing I did in conversation exchanges - pretending that I was in a real life situation like a job interview, a shop or a post office, and acting out that conversation with my partner. You will need to give them notice of which situation you want to roleplay, as people don't often pay attention to what language is really used in these situations and I often had to say "Actually, the shopkeeper always says..." Try acting out the conversation first to see how well you cope. Then ask your partner to correct what you said, and to write down useful words and phrases for that situation. You can then try the roleplay again, but adding some trickier and more ridiculous situations like trying to buy an elephant or applying for the job of CEO of Microsoft.
Controlled speaking practice
Another kind of more focussed speaking practice that you often get in the modern language classroom but rarely get in conversation exchanges is controlled speaking practice. This means trying to use a limited range of vocabulary (e.g. mainly feelings adjectives), functional language (e.g. just requests and offers), and/ or grammar (e.g. mainly "Have you ever...?" questions) as you speak. As this is not normal in everyday conversation, you will need to put a bit of effort into making controlled practice work. The easiest way is just to ask each other questions that you would really like to hear the answer to using the language that you want to practice, e.g. "When did you last feel angry?" or "What are the most irritating things about your siblings?"
You can choose the language that you want to practice from things you are having difficulty with, or from what has been or will be in your regular classes.
Language learning games are very common in class nowadays, but quite rare in conversation exchanges. That could be because there is usually no need to liven up chitchat in that way, but if you are going to try some of the more serious things suggested here you might need some light relief. Games are also especially good ways of making roleplays and controlled speaking practice more fun. In order for them to work in conversation exchange situations, you both need to have a realistic chance of winning the game, and it needs to be fun even in L1. For example, Scrabble will only work if you can only use words in the other person's language and you both have more or less the same level.
Two examples of games that could work quite well in conversation exchange situations are Revision Storytelling and The Definitions Game. In Revision Storytelling, you take turns trying to continue a story using as many words from one person's vocabulary notebook as you can. In the Definitions Game, you take one of the words that you want to revise and explain which one you are thinking of until your partner guesses what it is.
Email each other between meetings
This will give you extra practice, allow you to decide on the content of the next conversation exchange (and so save time for actual conversation and study on the day), allow you to correct your partner's written work, and give you some material to use for the ideas below.
Bring something in
If you run out of things to talk about or find that your conversation in unfocussed, it can be good to have something to take out of your bag and discuss together. This really could be anything at all. Examples include a photo album, an exercise from a grammar book, a favourite object, a holiday brochure, the lyrics to a song, or an email that you have received. If you have the right technology, it could also be a piece of music, part of a radio programme, recorded telephone call, or video clip. The important thing is not to be asking your partner to correct your mistakes or explain vocabulary to you all the time, so it is best to bring different things in every time you meet.
Another way of stopping things becoming too heavy is to limit the number of questions you will ask each other. Five is a good number, and trying to slim the number of queries down to this amount will also give you a chance to think about which ones are most important. The things that you plan to ask your conversation exchange partner about could be grammar questions, vocabulary explanations, useful phrases, or cultural tips. Again, you might want to give them some notice of what the questions will be in case they aren't easy to answer.
Look at each other's notes
Another way to help your partner out with the language that they are using and thinking about during the week is to have a look at their notebook or vocabulary lists. You could correct any mistakes, add to the explanations, or use the topics, tenses and vocabulary there to have a conversation or play a game.