For an expert review of this topic recommended reading is DNS Privacy Considerations.
For a full discussion of the options available please see DNS Privacy - The Solutions.
At the moment only a handful moment several of experimental DNS servers and two major operators support DNS-over-TLS and no desktop or mobile operating systems support DNS-over-TLS as a built-in option yet. (Many users have resorted to using Google Public DNS on 126.96.36.199 to bypass their local ISP for censorship/surveillance reasons but sadly it doesn't support DNS-over-TLS yet.) Work is in progress on building Apps No desktop operating systems natively support DNS-over-TLS as a built-in option yet but Android does. Several options are available though, see Clients (e.g. Stubby) for end users that will enable them to choose to use DNS-over-TLS and to select the specific DNS server they want to use.
It is possible that in future a different transport might be used for DNS (e.g. HTTPS or QUICActive work is also underway at the IETF on DNS-over-HTTP (DOH) but today the only method standardized by the IETF is DNS-over-TLS.