The easiest way is to use a table saw.
If you don't have a table saw, then yes, a circular saw would work pretty well.
If you want a nice straight edge clamp another straight board or other straightedge to the board so that it guides the saw.
To set up, first measure the distance from the edge of the saw's sole plate to the blade and then add the width that you want to remove from the board.
Clamp the guide board at that total distance from the edge of the workpiece.
For example, if it's 3 1/4" from the edge of the sole plate to the blade and you want to remove 1/2", you'd clamp the guide board 3 3/4" from the edge of the workpiece.
Then you 1) put on your safety glasses and 2) run the saw down the board with the sole plate riding along the guide board.
If you have a hand plane and a way to clamp the board on edge, that'll work too.
Draw a line 1/2" from the edge of the board and just plane to the line.
woodworking.stackexchange.com/users/492/Caleb
I am assuming you don't have a bandsaw or a table saw.
If you have a couple saw horses that you can use to clamp the board onto, then mark your line and using the circular saw to cut the line. if you leave just a little bit extra, then you can use the hand plane to true up the surface and fine tune the final size.
if the edge doesn't need to be pretty then just cut off exactly what you need with the saw.
Even a hand saw can be used, but it takes a little more practice to make a nice long straight cut.
woodworking.stackexchange.com/users/27/bowlturner
As Caleb mentioned, a table saw is the easiest way to shave off 1/2", since it will also guarantee that the newly-cut edge is parallel to a flat edge registered against the fence.
A circular saw with its base/shoe registered against a straight board also works, as Caleb mentioned, but can be a pain to set up because of the offset from the shoe to the blade.
(I can't tell you the number of times I spent 10 minutes or more measuring and fine-tuning the setup for a cut, clamped everything in place, and forgot to account for the offset.
Sometimes I realized it before I made the cut, but not always.)
To eliminate the offset from the equation and save yourself from a lot of wasted time and/or mistakes, consider making a zero-clearance straightedge guide or homemade tracksaw.
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A homemade or commercially-available parallel edge guide like the Kreg Rip-Cut would also work reasonably well with a circular saw and will require less setup than a straightedge for repeat cuts.
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Another solution is to use a router.
You can either use a straightedge guide similar to one of the circular saw guides, or you can use a (top-bearing) pattern bit or (bottom-bearing) flush trim bit.
Flush trim bits are slick because you can construct your project with the excess edge extending past the adjoining face, then use the flush trim bit to trim the edge exactly to the face.
Whenever you use a router, remember to take light passes.
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woodworking.stackexchange.com/users/49/rob
Another option that I haven't tried is to clamp another floorboard to it, offset by 1/4" and go along the edge with a flush-trim router bit.
Update: I have now tried this and it is easy and works like a charm.
I bought a cheap small router (the best selling one on Amazon, £40) and a pattern bit.
A pattern bit is the same as a flush cut bit but the bearing is near the router instead of away from it..
You can use either in this case.
Put the boards together on their edges in the floor, then tilt them so they are offset by the desired amount.
Clamp them on the top.
Then turn them over and get someone to hold them steady and cut!
If you have a workbench or something then use that obviously, but I don't.
The bit I got wasn't long enough to do the full depth (20 mm) but the router could easily have handled it if it could.
But anyway once you have cut half the depth you can just unclamp the boards and cut again using the already cut part as the pattern.
As Kromster says, if you need to cut more than a few mm use a jigsaw to do a rough cut first.
I didn't need to in my case because the timber merchants I found cut it to width for me.
woodworking.stackexchange.com/users/4394/Timmmm
Before I had a table saw (and I had misplaced my old circular saw in a move), I used a clamped down straightedge and a jigsaw* to cut the edge of a piece of plywood.
The edge was pretty rough, and would have needed some work with a sanding block or hand plane if I had been using it for something fancier than a garden cold frame, but it was a $30 tool that was at hand, rather than a (more dangerous) $40 tool I didn't have.
Best answer, as others have noted, is a table saw.
*
The hand tool, not
the table mounted tool also known as a scroll saw)
woodworking.stackexchange.com/users/4404/Steve
Table saw or circular saw.
If you're using a circular saw you can either use a straight edge, or use the gauge that is engraved into the base of your saw, provided there is one.
Just adjust the depth of your blade to barely come out of your piece, move your saw over on the piece of wood till the 1/2" notch is lined up with the edge, clamp down on the base with your thumb and forefinger, and rip away.
woodworking.stackexchange.com/users/4397/Squatting Dog 
I have a small 20" x 24" x 1" pine board that happens to be 1/4" to 1/2" too wide for my needs -- the 20" side needs to be more like 19.7".  What's the easiest/cleanest way for a beginner like me to shave this off? Would running a planer across the side work? Or would it work to take it off with a circular saw?
Easiest way for a beginner to reduce a pine board's width by 1/2"?
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woodworking.stackexchange.com/questions/1559
woodworking.stackexchange.com/users/648/fred
Table saw or circular saw  are recommended for beginners wanting to reduce a pine board's width by 1/2". Using a router is another option. It is possible to use a hand saw but that takes more practice. A table saw would be ideal but a circular saw would work. You could use a hand saw. Another solution is to use a router.
A table saw would be ideal but a circular saw would work. You could use a hand saw.  Another solution is to use a router.