The API is meant to be used by editing software, such as JOSM, Potlatch 2 or Merkaartor. It is not, in itself, user-facing. You are not expected to communicate directly with it yourself; rather, you use editing software to do that for you. The P in API stands for "Programming" and it means exactly that.
There is no Telnet interface to the API nor will there be. You could use command-line tools and text editors to communicate manually with the API if you really wanted, but it's very, very hard work.
Standard practice for making "programmatic" changes is to download the data using editor software (usually JOSM, which appeals to this sort of tech-savvy audience); save it as an .osm file; munge it somehow using your scripting language of choice; then re-upload using JOSM. However, this sort of editing can really hack people off if done badly, so exercise great caution if you're doing it in an area where other people are mapping.