Two things,
First that diagram will not work. Not only is the interface to the Arduino not right (as mentioned above) but the wiring to Vref is not right. This is a voltage reference, look in the data sheet to see what value it should be.
When you have sent a 16 bit word to the D/A you will have a DC voltage level on the output. So you have to keep on sending them to get an AC waveform. You also need a filter on the output of the D/A to remove the quantisation noise, that is the noise generated at your sample rate. You don't have to bother if you can feed samples at greater than 25KHz or so but otherwise you have to have one to prevent the high pitch whine.
To produce a sin wave you are best to have a look up table of how ever many samples you want, 20 is a good number, and feed them continuously into the A/D. To change the frequency you can do one of two things:-
- Change the number of samples and feed them at the same rate.
or - Change the rate you feed the samples in and keep the number of samples the same.