I believe you need a webcam to initiate video calls. The other party can initiate an audio/video call if they have a webcam. They will be able to send you video while you will continue to send them only audio.
What if you want to view incoming call/video, but not use your webcam/video. I only want to send audio.
Any particular steps I need to take?
A person decides whether to audio call you or video call you. When you receive a call you decide whether you want to answer the call (audio) or answer with video. You can change your mind anytime by toggling your video on/off.
If you want calls to be answered automatically, you decide in the Skype Options, Advanced Call settings, whether to just "Answer incoming calls automatically" (audio) or additionally "Start my video automatically when I am in a call".
So, do I need a webcam for my desktop to see other contacts? And do I need headphones to make the calls?
You do not need a webcam in order to participate in a video chat. So if someone initiates a video chat, you will see them, but of course, they will not see you. They can only hear you and read your IMs. If you do not have headphones, your speakers will generally be your audio output device. If you do not have speakers or any other audio output device, you will not hear them.
If you want to converse with someone, you will need a microphone. Some computers have built-in mics, others do not. Many people purchase headsets as they are a combination of headphone and mic. So if a computer is lacking audio input/output devices, a headset resolves that issue.