Before giving you the practical tips, it is important to first point out 3 things:
A) You should be 100% sure that you really need a co-founder (versus using a freelancer or employee which may be sufficient).
B) Investors usually take a deep look into the team and prefer founders that have worked together for some time and/or know each other for a minimum period (preferably those who’ve already experienced difficulties together before).
C) There is a reason that CBInsights found that the third most common reason cited for startup failure is “not the right team” and that the most common agreement that I draft as a startup lawyer/mentor is a ‘separation agreement’. The reason being that most co-founders eventually split – and not under nice terms.
In most cases, freelancers/employees can do what you need (perhaps the only exception is having a CTO when trying to raise capital from VC’s – and even this depends on the type of startup).
Regarding a limited budget, I am not sure why you feel that you need money to find a co-founder? If you have an idea/business that you truly believe in, and it has potential, you should be able to pursuad people to join you (in exchange for share/equity and/or future profits).
How to find a co-founder:
1. Go to networking events - some of which are dedicated to “co-founders dating/matching” - try www.meetup.com for this.
You can also try www.founderdating.com or www.cofounderslab.com or http://www.founders-nation.com or www.founder2be.com
2. Take part in chats in relevant forums (depending on the type of co-founder you’re looking for).
3. Consider joining accelerator/incubator programs for startups/entrepreneurs - some of them connect between founders.
4. Contact head of programs at universities and tell them what you’re looking for. Today, many universities and cities have startup programs with a lot of talented participants (or speakers) who might be the perfect co-founder for you.
5. Talk to friends and family and let them know that you’re looking. This helps expand your network. Post a message on www.LinkedIn.com .
I've successfully helped over 300 entrepreneurs. I'd be happy to help you. Good luck