You should start taking registrations at least 2 months before the actual starting date of the league. It is advisable to offer both online registration as well as in person or paper-based registration. Forms may be basic or very involved with many fields beyond just the participants information. Some forms have sections about parents volunteering, willingness to be a sponsor, liability disclaimers, etc. Find or create one that works for your needs.
You should charge a registration fee. If something is free, psychologically it is often not considered as valuable as something that has a cost. Fees give the perception of value. Many youth sports have taken that notion perhaps a little too far and it is not uncommon to find programs that charge well over $50 for a registration fee. If you have several good sponsors, a reasonable registration fee for your youth Horseshoe league might be around $20.