Vedantic philosophy is simple and focuses true self. Its aim is to bring a person to conscious or self-realizing, and yoga is used as a practice methodology to achieve this realization. It requires a higher amount of concentration on inner-self than some other forms of meditation. The purpose of the philosophy is to create an extreme level of patience and acceptability.
In practicing this method, you can focus on gaining spiritual knowledge, either using yoga as a methodology or otherwise. This is because in this tradition promotion of the belief that makes oneself free or reaching to the level of self-realization is only possible through spiritual knowledge. It refers to a sort of freedom of spirits.
Although you can do Vedantic meditation during any time of the day or night, the most recommended time by its gurus is just before sleep. This helps you clear your inner-self of all the karmas of the day and purify yourself just before the sleep. Morning time is also an important time when most of meditative practices can be done, and it is also suitable for Vedantic meditation.
You can start practising Vedantic meditation on your own but must have knowledge of its true purpose. If you are not confident to start yourself, you can start under the guidance of a teacher. It can be probably more beneficial since the teacher can guide you through all the process and help you improve yourself in the quality of meditation sessions.
Make sure you get better at the level of your inner focus and concentration with every session and if not try to get help from a teacher. Freeing yourself from all karmas of the day while practising the meditation is actual purpose of the philosophy and you should be able to achieve this. If you somehow are experiencing some problems then contact a learned person, who has thorough knowledge of these philosophies and their practices.