I instruct at an airfield with the luxury of grass and tarmac landing strips so can get the best of both worlds....
Aeroplanes "land" just the same on grass as tarmac but as the previous posts say the techniques on final approach can vary - it depends on the condition of the grass and it's length, all the stuff we learned way way ago in performance. Grass however is more forgiving in a cross wind as the students who just will not get the nose straight in the roundout and flare like the fact that the aeroplane skids sideways much easier and lets them off a crap approach - something they come a cropper a when trying the same on "nasty" tarmac. True also that wet grass is like landing on an ice rink - be very clear in using gentle braking, any departure to the side is almost unrecoverable since our steeds handle like drunk supermarket trollies at the best of times. Same goes for mud too and keep the power on during the roll out otherwise it can get embarrassing when you sink up to the struts.
Short field techniques are very good though I wouldn't say they always must be used on grass - once again it depends on the length and condition of the strip. Look in the POH to find the correct speeds (eg C150 is 55kts I believe with full flap for short field approach and they're fab fun too in these!!) but you must be very active on the throttle - since you have almost nae airspeed (even more so in a good head wind) and very draggy, you must not let the IAS drop below that fig. As soon as you cut the power the chariot will land whether you like it or not so don't until you want those tyres to touch terra firma.
The landing roll however is much different to tarmac - be prepared to be bounced about a bit even on the most billard-table like of runways. Any bounces on the roll (if not huge) due to un-eveness can easily be controlled in the ususal manner. Taxying across them can be interesing when they've ben rutted - think of a Dalek going across a ploughed field and you have the picture.
Finally, if you're not happy, bin it and go around!!
