Erasmus, generally, is to have the opportunity to study abroad, therefore learning new contents and other types of teaching methods, getting access to a new language and culture, and to enjoy the experience of traveling.
Of course, each person has its own motivations. I see a lot of students here that don't care about the learning/studying part, and they spend their time in parties and whatever. Of course, fun is also a major part of this experience, but I feel quite sad seeing them, well, not wasting, but just with other major reasons.
Most topics are quite obvious, but all of them are important. :)

1. Get very well-informed about all the available countries, universities and programs in your university of origin.
Decide what do you want to do in your License/Master/Doc, your objectives, how long do you want to stay, etc.
Choose very well the country that you're going. Make sure that you'll put an effort to learn the language and culture, and get informed about what you can and what interests you. Location, weather, food, costumes, cultural attractions, etc.
In my case, I was pondering between France, Austria and Italy. Though I really wanted to go to Austria, the program wasn't that interesting, unfortunately. Once I saw the one in Rennes, no need to say more. :)

2. Talk with your professor/coordinator about everything you want to know or clarify, and respect all the advices that he/she gives you.

3. Respect all the deadlines of paperwork, things to deliver, etc. The sooner, the better. All these things take time to process.

4. Do copies of every single document that has, basically, your name on it, and do it before you go.
Photos, ID cards, Driver's license, Bank accounts, Birth certificates (believe me, I had a lot of stress to ask one when I needed it), Contracts, whatever. 
Do 100 copies of each. Minimum.

5. If you don't know the language already, do what you can to travel there, at least, with the basics. 
How to ask information, how to indentify yourself and your needs, etc, etc.
There's probably language programs, courses, etc., in your University, or you can check at schools and academies. You can also buy books or do it online. 
Everything is up to you and your determination. 

6. Normally, the exchange University offers student lodging options. You can either apply to that or search by yourself places where you can stay. 
Needless is to say that is better if it's close to the University. Even if the rent is higher, you save on transportation and time.

7. Save all the information that you have about the University where you're going and all the contacts that you had with it.
Normally, they contact you by e-mail or correspondence.
It's better if you create a file where you can keep all that data and, then, create a list of what you need to do when you're there. Example: dates of reunions, presentations, welcomings, etc.
Try to be present in all of that, it's all part of the experience and it's always useful. 

8. Check with a lot of time in advance the various offers to go to your destination.
If you want a low-cost ticket, even if it's cheap, don't forget that you have to pay extra fees to take hold luggage. 
I, for one, went by bus, where I could take whatever I want without paying, though the journey is very long. (And it's just Portugal to France, 26h...).

9. When you start packing, take what you need and what is very likely that you will need. 
If you go to a cold country, it's not needed to take a lot of summer/spring clothes, for example.
You can either make a list, start selecting what you're not going to take or, if you think you'll need something that you don't have, you can start checking online, for example, to see it it's cheaper where you live or in the country where you're going.
Either way, do everything with time

10. Plan your journey. Your arrival, where do you go after, what route/transports you must take, and useful locations that you might need. (Example: supermarkets, pharmacies, restaurants, information posts, post office, etc). 

11. When you're already there and settled, and after the stuff mentioned in the topic nº 7, enjoy!
Thanks to the few useful tools in social networks, there's Erasmus groups on Facebook to help welcoming all the new students, where events are created, shared information that you need, and also to help you practice the language and meet new people - because that's also a big part of this great experience.

12. Put your efforts in this exchange. It's another language and another system, probably, so really organize your time and your studies to try to get good results to represent positively your University, your country and yourself. 
Talk with your teachers if you don't understand something, normally, they comprehend your situation and are available for you.

13. Don't get frustrated if something doesn't work at the beggining, like your documents, informations, cards, etc. You'll probably visit the International Services office frequently, and that's also a (boring) part of this, but it's better if you get everything straightened quickly than to get more problems in the future. 

14. Explore! Enjoy the time that you're there to visit the city where you're in, absorb all the culture, how people are, etc.
There are also cheap ways to visit other parts of the country. 
Covoiturage it's an example that's getting more and more famous and used throughout all Europe. 
There's also cheap train tickets, discounts for studens, etc. 
Internet is always there for you. 

15. (Just to finish in a pretty number) Create good memories of all this. Meet new people, hopefully, make good friends, share what you can, and make a good chapter out of this in your life. 
The objective of all of this is to LEARN! :)
"Where did you go, if I may ask?' said Thorin to Gandalf as they rode along.
To look ahead', said he.
And what brought you back in the nick of time?'
Looking behind', said he."