When using libcurl's "easy" interface you init your session and get a handle (often referred to as an "easy handle"), which you use as input to the easy interface functions you use. Use curl_easy_init(3) to get the handle.
You continue by setting all the options you want in the upcoming transfer, the most important among them is the URL itself (you can't transfer anything without a specified URL as you may have figured out yourself). You might want to set some callbacks as well that will be called from the library when data is available etc. curl_easy_setopt(3) is used for all this.
CURLOPT_URL(3) is only option you really must set, as otherwise there can be no transfer. Another commonly used option is CURLOPT_VERBOSE(3) that will help you see what libcurl is doing under the hood, very useful when debugging for example. The curl_easy_setopt(3) man page has a full index of the over 200 available options.
If you at any point would like to blank all previously set options for a single easy handle, you can call curl_easy_reset(3) and you can also make a clone of an easy handle (with all its set options) using curl_easy_duphandle(3).
When all is setup, you tell libcurl to perform the transfer using curl_easy_perform(3). It will then do the entire operation and won't return until it is done (successfully or not).
After the transfer has been made, you can set new options and make another transfer, or if you're done, cleanup the session by calling curl_easy_cleanup(3). If you want persistent connections, you don't cleanup immediately, but instead run ahead and perform other transfers using the same easy handle.
curl_easy_init(3),curl_easy_cleanup(3),curl_easy_setopt(3), libcurl-errors(3), libcurl-multi(3), libcurl(3)
libcurl(3), libcurl-multi(3), libcurl-share(3), libcurl-tutorial(3).