networking's purpose is not to just ask for jobs, however there is no harm in letting your network know you are looking for opportunities and help/leads would be appreciated. The stronger a relationship you have with a person the more help you can expect to get.
Its not about sounding desperate, those close to you just tell them you are looking for opportunities and to let you know if they know of anything. Make your request more specific, help ppl help you. i.e. not just looking for an internship but looking for an internshio in a hightech company in the area of marketing especially marcomm.
for people you are not that close to, ask them if you can talk to them to get insights about their company and industry, especially for target companies, or about current career trends for people who are in the types of roles or depts youa re interested in.
asking people for a job puts them on the spot, they may not be able to help, they may not have anything and they may not know you well enough, but people in general dont mind helping, its all in how you approach them.
Thanks for your advice. But what would you suggest if you really dont know what area you are looking to work in. Personally I am not sure, and I have read that telling that to people is not a very good idea.
If you dont mind, could you give me example of how one would talk about it without being really obvious that you want their help.
One of my mentors has told me that he has never asked for anything and has always been given the opportunities and positions he currently has in his professional life. I don't know if that would work because his network is built on years and years of experience.