As with any marketing strategy, before using Google AdWords think hard about a) whether it is worth the money your charity will spend, b) how you will track the response and c) what you will define as a positive outcome.
Find something to track that can be measured easily, such as donations, sales, volunteers or service users. To track this data you will need some type of website tracking software. I use the free tool Google Analytics to track traffic on my website.
If you are hoping to raise donations from your ads, create a new donation landing page that links to an online donation service with a campaign code so you can track all donations that resulted from your Google Ads. Think about how many new donors you hope to obtain through your campaign and how much money you could fundraise from them.
If you sell products online, then you could add an identifying parameter to each ad by adding ?referrer=googlead1 to the URL that people go to when they click on the ad. Your online shopping system should be able to log this information with the sale. Think about how many new customers you hope to obtain and how much profit you could make from them.
If you are tracking new volunteers or service users, create a new page on your website with a contact form that emails all responses to a particular email address. Think about how many volunteers or service users you want to attract.
NB: If you are a charity you can get free Google AdWords for at least three months.