Does browsers use one-way or two-way SSL/TLS when I browse to a https address?
Typically you are using one-way SSL/TLS because your browser is checking the certificate of the server but the server is not checking for a client certificate pre-installed in your browser.
When using mutual authentication the browser verifies the server's certificate just like a typical one-way connection but an additional step is involved where the server verifies that the client has a certificate which allows them to access this system. This is not common and requires you to install a client certificate.
The browser can do both easily but if an additional certificate was not installed the authentication is probably only one way (authentication of the server). In both cases, all traffic is encrypted in both directions the one-way or two-way part just refers to the authentication components.