Due to time constraints, the best time to learn a new language varies for different people. Some may find more free time after they are retired, or some want to learn a new language early in their career to gain better prospects. However, it is possible to come to some conclusions on when is the best time to learn a new language for most people.
As a rule, it is better to learn a second language when you are younger. Obviously, your ability to retain learned material is better, and not only that, you are able to learn at a faster speed. If you are surrounded by native speakers, you will naturally pick up the language quickly and find it easier to grasp it rather in a constrained classroom setting, for example.
It has been proven that a child who learns many languages when he is young will also be able to pick up new languages at a faster rate when he grows older. This is because his mind is trained well linguistically from a young age. It becomes more flexible as he or she learns more.
If you are an adult an about to migrate to a foreign country, for example, then that is the best time to start learning a new language, the language of the country you are going to. You will become confident in your ability to speak the language once you enter the country.
Do consider what your goals for your new language learning, and strive to achieve it! It's a whole world out there in languages.