You may want to set aside a few things prior to getting started:
    News papers to place on the ground or bench,
    old paint cloths (it gets messy)
    time, it usually takes about an hour maybe two for a large piece..
    Less than that for bird baths and small figurines...

Materials list:
    Portland cement
    Exterior Latex house paint
    bleach
    pressure washer (optional)
    1/2 gal to 1 gal container for mixing the paint (with a lid or plastic wrap)
    1 large paint brush (disposable.. it will be toast when done)
    Can of the Better grade Auto Bondo (optional)
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Prep of the item prior to repair and painting:
    Clean and dry the concrete statuary / birdbath / water feature.
     I use the pressure washer
    You may want to use a little bit of beach mixed with water to kill moss and algae.

The piece has to be dry to do any of the following..
      (We usually just let it set in the shed for a couple of days.)
 

For broken off chunks or splits
    use the better Bondo putty for cars (used for fiberglass bodies will take more moisture)
    bondo will cure in a few hours and you can scrape the seams and is ready to continue

The mix for chips and dings and repainting:

    1/3 part Portland cement (the powdery gray stuff used to make concrete any brand)
    2/3 part exterior flat latex house paint
    (usually white but other colors work realize that the gray cement power will mute the color)

Screen the cement to remove lumps new works better than the stuff that has been sitting around and has gotten even a little bit of moisture in it.. (Gets grainy)

Add a little water to the cement first then mix in the latex paint in stir well
 

cosmetic repairs:
if you have minor repairs like the tip of a nose or a small chip off the thicker mix will work great to re-sculpture the part that is missing  ( up to the size of the end of your little finger)

The finial covers up and make over to look like brand new:
At this point the mixture is too thick to use to paint or refinish the cement statue.. Add more water and stir well..

If the piece is made up of several sections you will want to paint all of the sections!

Turn the parts UPSIDE DOWN and paint the undersides first and let dry (2 hours usually)..
Then turn them over and do a nice finish coat on the side that shows