Hosting a block party is an effective way to become familiar with the girl who lives on your street, as are delivering fresh treats, spending more time outside, asking to borrow something and being civic minded. Other ways include paying attention to flyers, hosting a cocktail party and organizing a play date if you both have children.
Hosting a block party can be as informal as posting a flyer in the neighborhood and inviting neighbors outside for a BBQ. To host a more formal block party, plan around a theme. Some ideas of themes include asking families to wear matching colors or bringing tropical food dishes for a beach theme. Determine a central location that can hold many people, and contact city officials to know what is required to host a block party, if anything. Then invite the girl you're hoping to know better.
Delivering homemade goodies to someone is apt to leave a good impression; including a simple card with contact information can help assure future communication.
Flyers with information about neighborhood events often wind up in mailboxes and front doors. Before throwing these away, check to see if any of the activities might be interesting to you and to the girl with whom you're hoping to connect. For added security, invite her to attend with you.