Investing in a 403(b) is done by making contributions via payroll deductions and selecting investment options from among the available choices with your custodian.
Payroll deductions on a pretax basis are routed into your 403(b) account with your consent. This can be done by telling the payroll department what percentage of your compensation you would like to send there, or by telling the plan custodian company, who tells your payroll department.
It can get interesting if you have multiple vendors within the same plan, but this is gradually becoming outdated. This has been allowed because many 403(b)s are not subject to ERISA, and the freedom from oversight and auditing requirements has made these plans a little more creative than the 401(k)s you may be more familiar with.
Some 403(b)s also allow after-tax, Roth-style contributions. Whether pretax or post-tax, your money will be directed into the investment allocation that you have chosen with the vendor or custodian that holds the plan’s investments.
The investment options available to you in your plan are agreed-upon by the vendors and your employer. Beyond that, the freedom to choose, and the investment risk, is the employees.