Your question is kind of broad, so I'll answer broadly. Narrow down your question (or post a follow-up) so we can help you better.
Is it possible to making a posting to Craigslist through my own website?
It depends, there are two major ways, but most websites block these so I suspect Craigslist does too.
1. Clientside
Your visitors become visitors of craigslist.
You take the form that you find on craigslist, and host it (the html code) on your site, but with the form 'action' pointed to theirs.
They'll probably block these, based on the REFERER, a session key or something alike.
2. Serverside
Your server acts as a client for Craigslist.
You host the form on your server, and the processing page as well. After you've captured all the input, your server will now act as a client to Craigslist, using indeed for example php curl.
You should try if 1 works, if not, start coding on 2. If you're stuck in a specific part, post a question and we'll help you further.
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