Most of the questions I get are around meeting new folks:
"How soon before I can ask for a job/lead/idea/etc.?"
For sure not at the beginning of building a relationship. While there is give and take in all our interaction (friends, coworkers, family), relationships are not bank machines and you can't build a connection without first establishing a bridge.
If you think about why you answer other folks' requests for help, it's likely because they have been there for you along the way.
I prefer to start by approaching new relationship not for what they can bring to me but what I might bring to them.
"Why would anyone want to talk to me?"
As per above, for what you have to offer! However, the best thing I've seen folks do is offer their full attention and listen.
We don't know just by looking who is or isn't going to be an interesting addition to our circles. Everyone has something to offer but sometimes timing is poor and the connections slips or doesn't happen. This doesn't make you any less valuable/interesting than anyone else in the room.
You can ask your new acquaintances questions (preferably beyond the "so what do you do?" genre) or probe for opinions about the speaker/presentation (work or kid's soccer game), the setting (could be a grocery store line!), the book in their hand... And then be genuinely interested in the response. Most folks will happily talk away to you at that point.
If you are at a formal networking event, consider first why you want to speak to others. Set a goal and probe the room.
"Do I just walk up to strangers and introduce myself?"
If they are at a networking event, then it's a given that you're expected to talk to strangers.
If you are moving through the various settings of a day, then yes again - however those interactions often start with a shared glance/smile or comment and then one or both of you can choose to carry the conversation forward.
If you prefer, a less direct approach in any situation, consider asking a friend to make introductions for you. (in dating, that's the 'wingman')
"Do I have to meet new people?"
Nope. You don't have to do anything. You don't have to even read the rest of this post! Networking isn't medicine; it's a philosophy.
"Where can I meet new people?"
Everywhere. Elevators, meetings, line ups, bus stops, you name it - folks are there for the meeting.
Keeping yourself open to encounters and enjoying the interaction are all it takes.
I've got lots of networking tips throughout this blog but the best tip I have is take a breath and smile at folks; it's really that simple.