When it comes to getting hired, it's often all about who you know. Your personal connections with your neighbors, friends or family may open doors to new jobs, and in some cases, the neighbors themselves may be the ones to hire you. Every job you do can be fodder for a resume, no matter where you found the opportunity.
Whether you did lawn care, babysitting or a job in a more professional capacity for your neighbor, the plain fact is that you rendered services and got paid for the work. It doesn't matter whether the person is your neighbor, grandmother, cousin or a total stranger. You did the work and should most definitely include it on your resume, especially if that job pertains to another job for which you're now applying. Hiring managers are not going to know you or your neighbor, and even if they do make the connection, it still doesn't change the fact that you have that work experience.
There's no one right way to format a resume, but the most traditional format is the "Work Experience" format that lists your most recent jobs in reverse chronological order near the top, followed by a section on your education, interests and references. If you're using this type of resume format, list the job you did for your neighbor among your jobs in the work experience section, the same as you would for any other job. Type the job title, such as "Lawn Care Worker," "Nanny," "Bookkeeper" or whatever it was in bold lettering, and then type the dates of employment. If your neighbor has a business name, type that next. If not, include her first and last name. Following that, type a few sentences about the nature of the work.
The other common option for resumes is to use a "skills-based" resume, which is a good choice for people who have large gaps in employment, have done a lot of odd jobs or may not have the specific job experience specified in a job posting. With this resume type you place more focus on the skills you have and not the employers you worked for or the dates you worked for them. This can be a way to include the skills you gained from working for your neighbor without having to mention the neighbor at all in the resume. Create a "Skills" or "Competencies" section near the top of the resume, and then type a bullet-point list of the skills you possess. This could include things such as carpentry and plumbing or more abstract concepts such as strong leadership or negotiation skills. People who use this type of resume typically follow the skills section with a brief list of past employers and the years they worked there, in which you can include your neighbor's name if you so desire.
If an employer is really interested in you, chances are she's going to ask you to provide employment references. Talk to your neighbor ahead of time to let him know that you've included the work you did for him on your resume and that employers may be contacting him to talk about the job. While you won't be able to control what your neighbor says to the employer, you could ask him to avoid mentioning that you're a neighbor. This may help avoid any awkward conversations about favoritism.