What 29 CFR 1904.35 requires (plain English)
Most of Part 1904 is about what the employer writes down. 1904.35 is about the people the records describe. Its first half makes sure injuries get reported at all. You need a reasonable procedure for employees to report work-related injuries and illnesses promptly and accurately, and the rule draws the line itself: a procedure is not reasonable if it would deter or discourage a reasonable employee from accurately reporting a workplace injury or illness ((b)(1)(i)). Each employee is told how to report, that they have the right to report, and that the employer is prohibited from discharging or discriminating against them for it ((b)(1)(ii), (iii)). And the employer must not retaliate ((b)(1)(iv)).
Those words date from OSHA's final rule of May 12, 2016 (81 FR 29624), effective August 10, 2016 for this section. The preamble explains that the reasonableness language clarifies a requirement already described in a 2012 OSHA enforcement memorandum, and that the duty to inform employees of their right to report without retaliation can be met by posting a recently revised version of the OSHA poster.
The second half is access. Employees, former employees, their personal representatives and authorized employee representatives (a collective bargaining agent) can ask for the 300 Log of an establishment where the employee worked. The copy is due by the end of the next business day, with names left on except for privacy concern cases ((b)(2)(iii), (iv)). An employee gets their own 301 Incident Report on the same clock; a union representative gets only the section titled "Tell us about the case," within 7 calendar days ((b)(2)(v)). The first copy is free ((b)(2)(vi)).