A referral can definitely improve your chances!
Nowadays, networking is often reduced to LinkedIn connections and personalized emails, but some tips remain the same:
be honest and be yourself
Build relationships naturally
remove the pressure of proving yourself all the time
Don’t be pushy, don’t ask directly for a referral
1) If you contact 10 people, 5 will answer, 2 will agree to schedule a call, and maybe 1 person will stay in contact with you and eventually refer you.
Not everybody will be willing to help you. The problem is not you, so don’t let that put you down.
From the previous rule: contact more than 2 people to obtain replies.
2) First contact people you know- you never know who knows who!
3) Follow up with people you’ve emailed and they didn’t answer you until you get a yes or a no.
4) Prepare a strong CV.
In case one of the consultants is willing to help you, he/she might ask you to send your CV, and you should have it ready.
5) You should always be ready to pitch yourself.
Networking is about building strong and long-lasting relationships and having a reputation as a good worker. This kind of bonding requires commitment but also a real drive to do that, based on a real interest, not just the potential merit of a relationship. So be wise in choosing who you want to connect to and who not.
I'd like to point out:
your goal in networking is to schedule a call with a person. The call will be like a fit part of the interview where you'll be able to present yourself, understand whether you'd be a good fit for the company, and ask questions about the experience / company / any advice (which indirectly can mean the referral)
Consultants don't always have time to check their LinkedIn, so personalized emails are preferred if your target is a referral
However, if you're networking in the LI - try to find things you have in common and build your conversation around them.
Remember that even If now you're networking for your personal interests, one day you might help somebody from your network, too.
It definitely is going to take some time, but if you are going to apply 1 or 2 years from now, don't rush. Spend the time wisely and value the quality of the relationship over the quantity.
Hope that helps!