This works equal to Ultimate Team. You have 5 ranking-matches to get ranked into a divison. To get ranked directly into division 3 you need 4 wins out of the 5 matches. I reached division 2 with 4 wins and 1 draw.
There exist various informations (thanks to the guys who commented) about different rankings with 3 wins and 2 draws or even only 1 draw. Head for 4 wins to be nearly sure. It seems that also the matches themselves have an impact to the ranking. Some players wrote that they did only get ranked in 4 with 4 wins, so to be really sure you should aim for (five) clear victories.
In the meanwhile it is confirmed that there is no second chance for the ranking-matches the next week. As stated by others you should play a lot in the division you got ranked and based on your wins/draws/losses you will get promoted after the two weekly lasting "event", the last ones even were shorter (one day). Based on what we know by now is that you should win as much matches as possible to get promoted. If you get a green arrow next to your division you get promoted. Achieving rank 1 for the event does not seem to affect anything about getting promoted but to be sure it can be helpful to also get enough points for it. It is also confirmed to be possible to get promoted more than once after an event. Try your best!
To win matches in Volta I highly recommend you to play the debut and lots of battles against the AI first to acquire strong teammates and to get your players skills up to 90+ (so you also can get the other achievements for Volta) and to get confident with the mechanics of the mode (which shots are most powerful, best dribbling and passing styles...).
In my experiences it is not necessary to skill around to much, simply pass a lot and try to place save shots to score (far post while running to the goal from one side at about 3-4 metres distance). After some pratice it should be possible to win four out of five matches with a good team. The most players with experience from Volta20 or FUT should not have bigger problems with this since the level of the opponents I experienced was not that high.
The first bigger update seems to have made the matchmaking issues better. I read reports about lost matches that never started and experienced long waiting times because in most cases there is an error in creating the match or after the loading screen it aborts with some connection issue before. Try it out by yourself and report how it works. If its not comfortable enough for you, wait for another big update to play on.