Redoing a floor?

A small pry bar will do the job.

This is what nail puller bars are for. Better than hammers, easier to use, last forever. 

A small pry bar will do the job.

Get a wonda bar or other flat pry bar.  Slip it under the wooden strip, but a cushioning material of some sort under the pry bar where the curve meets the straight part.  apply pressure to the bar and the wood strip with lift up fairly easily then move on down and keep repeating it till the wooden strip is up.  It should not damage the floor at all and the job is rather easy to do.

Use a "5 in 1" tool or wonder bar and don't scratch the hardwood if you have it. Start at one end and move down to the next. Don't start in the middle because they're harder to pull up and will break 

Get a good set of electrical side cutters.  For cutting electrical wire.  They will grip and there is enough lever there to pull out most nails.   To remove the wood strips, a hammer and a chisel or a narrow, stiff putty knife should get the wood strip up.  You will need a duster to sweep up the mess and a dust pan and a trash can to put it in.

You just have to stay at it with a hammer and small crow bar type tool.  There are a zillion nails in those strips in order to hold the carpet in place.

Hammer and a bolster (or old chisel), or a jemmy.

Use a small crow bar, also called a cat's paw.