Method 1: Reciprocating saw
The worst part of regrouting is the incredibly tedious, tough hand-scraping to get the old stuff out. Now you have two much better options. If you already own a variable-speed reciprocating saw, try a Milwaukee Carbide-Grit Grout Blade (No. 48-08-0415; about $14 through our affiliation with amazon.com). It works really well. Just make sure to use the slowest speed until you get the feel of the process.
Method 2: Oscillating tool
If you don't have a recip saw and you're dying to get your hands on a new oscillating tool, this is your chance. The Dremel No. 6300-03 Multi-Max and the Rockwell RK5101K SoniCrafter kit are two tools that include grout removal blades. The Dremel Multi-Max is available through our affiliation with amazon.com. The Rockwell SoniCrafter is also available through our affiliation with amazon.com.
An oscillating tool (bottom photo) is a bit easier to control than the recip saw because it's smaller and has a much shorter blade stroke. Plus, you can rotate the cutting head, so it's a tad more versatile.
With either tool you'll need to be careful not to chip the tile. We've tried both systems and they work equally fast. The oscillating tool does get you a bit tighter into corners. With either method, you'll still have to scrape some areas by hand.