You can create your own organization as a legal entity (see article 51 of the civil code). To contract with a student you will face from established firms. Themselves to act as the operating company (the teacher) If tutoring is for you – a family business, the second person can be issued as a hired worker.
Find out whether you need to obtain a license for the provision of services in the educational activities in which you plan to specialize.
If you do not plan to expand their business and to do tutoring together with someone, please fill out the tutoring as self-employment. In this case, you are registering as an individual entrepreneur.
The license in this case, you do not need, because from the point of view of the law (clause 2, article 48 of the Law of 10 July 1992 № 3266-1) you are engaged in individual pedagogical activity.
Determine your economic activity. It is necessary for the proper execution of the payment of taxes. Tutoring services generally fall into STS (simplified tax system) in accordance with clause 2 article 346.25.1 of the tax code. According to this scheme of taxation you will have to pay the state 6% of the profits.
To determine which type of tax you must pay, check the national classification of economic activities (OKVED). For sure you will fall into these categories:

-110000 Services in the education system;

- 111000 Services in preschool education;

-112000 Services in the system of secondary education;

- 113000 Services in higher education.
Note that contrary to popular belief, under UTII (single tax on imputed income) the work of the tutor misses.
Having individual enterprise, with each student you are entering into a contract of compensated rendering of services (article 779 of the civil code).