Speaking as someone who gets messages like this most days, I think there's a very definite right vs wrong way to do this. If you do it the right way, people will be more inclined to help you and really go out their way to do so. The inverse is also true, though - if you approach it badly, chances are someone will help minimally or not at all.
Few pointers, again from the perspective of receiving messages:
- tell me a bit about yourself! Context for your messages (a) helps me get to know you as a person and as a candidate, (b) gives me a much better understanding of the best ways I can help you, way more than you think it will and (c) means I'm more likely to invest time and energy in helping you as I feel like I'm dealing with a person rather than a robot applicant.
- tone is incredibly important. Bear in mind that you're messaging someone who's a perfect stranger... overfamiliarity is probably the number one thing which grates on me if someone reaches out. That's not remotely to say that you need to be a grovelling wreck, begging for the slightest shred of attention and time - in fact, the opposite is true - but a level of professionalism and remembering that you're not chatting to your best mate is important.
- "please" and "thank you"... you'd honestly be shocked the number of messages I get where there isn't a please or thanks in sight. Call me old fashioned, but manners cost absolutely nothing and there's no real excuse for not saying please or thanks in a message.
- if someone responds to you, FOLLOW UP! I must admit that I hate it when I respond to someone via LinkedIn to help them out after they've reached out, they then read my message and don't bother to respond. Again, not asking for Shakespeare's Sonnets in thanks but just a little note or even a follow up question is always greatly appreciated and I'm 110% more likely to want to help you again in the future. It's also highly beneficial for me to know that something I've said is or isn't helpful, so I can best help people who get in touch!
One final thing while I'm on the topic anyway is the issue of asking to see someone's previous, successful, application. Personally, I would never ask for this unless I knew the person really well. I think, generally, if someone helping you is happy to share their application, they're likely to volunteer to do so. I personally don't share my applications (with strangers at least, I've shared them with close friends who are applying to places) for a few reasons: partly because I think it has the capacity to distort the recruitment process which isn't the right thing to contribute to, partly because I don't know Joe Blogs well enough to be sure that someone won't just copy and paste my application to try and pass it off as their own (which would also reflect badly on me). Mostly, though, because I always made my applications highly personal and put in a lot of personal, often sensitive, information into them and that's not information which I would necessarily feel comfortable sharing with someone I don't know well (who's likely to know this stuff about me anyway).
I really hope I don't seem like a self-important a--hole with this. Personally, I love helping candidates whenever I possibly can (my single biggest reason for being a part of the team here). Networking is definitely a skill, though, and there are definitely factors which can make you better at it! Hope this is somewhat helpful, sorry it ended up going down a bit of a rabbit hole!