Single supply amplifier for driving 8ohm, 0.7W speaker
Consider a simple push pull stage like this one that I have modified from a picture on the internet (but take note of stuff I've said further down): -



There will be some cross-over distortion but, because the output transistors are "within" the feedback loop of the op-amp it won't be too annoying.

However, take note that the LM358 is really poor at delivering a high level output voltage on a restricted supply voltage - I would definitely look for an op-amp that has a rail-to rail output.

If you got a R2R op-amp, the output voltage to the speaker would be about 3.5 Vp-p (sine wave maximum) and this is an RMS of 1.24 volts hence, the power into an 8 ohm speaker would be limited to about 200 mW with some distortion.

However, if it were a square wave fed to the speaker, the power out would be about 380 mW. 


  I am trying to build a simple amplifier to drive an 8ohm, 0.7W speaker
  using a 5V single supply.


If you definitely need to get close to 0.7 watts then consider using an output transformer or a bridge amplifier. The problem with a single push-pull stage is delivering the peak-to-peak voltage from a 5 volt limited supply.