Most European Universities allow applications until late March and some until late June. In America, most applications must be submitted until January, so it is good to plan ahead.
If you are planning of submitting applications to both European and American universities I think you should start all the arrangements by the end of the summer of the previous year. That is to say, August or September is the time to start over. I guess you should plan everything so that you are able to submit an application in December or January. Even if the deadlines are very far ahead, it is important to apply early. Some universities, such as Cambridge, assess applications as they are received. So, places are being filled even though the application deadline has not passed yet.
Every top university asks for two exams: the GMAT and an English Test (if English is not your native language), such as TOEFL or IELTS. Bare in mind it may take some time to schedule these exams. Where I live, there is only one date per month to take the IELTS. That means if you don’t get the score you need, you’ll have to retake the exam, loosing at least a month in the process. The same goes for the GMAT.
So, I would say you should have your tests made by November. That will give you a month or two to get the application documents and to think about all the essays and amazing questions they have for you. American Universities usually have more essay based applications. European Universities require less effort (and imagination!) to fill their application documents.