For the time being, Google will only price match online prices from just four retailers: Amazon (sold by Amazon.com), Best Buy, Target, and Walmart. Requests must be made within what Google refers to as the buyer's remorse period (15 days for most goods, 30 days for the Nest Thermostat), the model or product number has to match exactly (same color and storage, where applicable), and the advertised price must still be in effect at the other online store when a price match request is made. All requests are only handled via chat or a phone call, and the burden is on the customer to provide product links to Google for verification (no screenshots, pictures, or PDFs). There is a maximum limit of two requests per customer per product, with no rain checks accepted.

When it comes to phones, only the unlocked, non-carrier models are eligible for price matching. Google posted a list of other exclusions on its site, which has been copied below:

Excludes: Contract mobile phones or financing deals; special daily or hourly deals; pre-order or trade-in offers; wholesale or educational pricing; mail-in, coupon, or gift card offers; pricing errors; product bundles or free items; bundled services or support; clearance, open box, refurbished, or pre-owned items; products shipped or sold by third-party sellers on competitor’s website.
Once Google approves the price match, the difference in price will be credited to your original method of payment.

Source: Google Support