How to build a transmitter using a VCO module
An antenna needs to be some fraction of the wave length of the signal being transmitted or received. Quarter length, half length or single length work the best. A wire should work just fine at the beginning. 

To calculate the wave length the formula is Speed = Length X Frequency. Radio waves are regarded as moving at the speed of light 2.997 meters/second. 

I'm not an RF guy but all of the RF equipped boards I've dealt with recently have a series capacitor in the path between the transmitter and antenna. 

The oscillator itself is going to need some bulk/decoupling capacitance at the power input across VCC and GND. A mixture of aluminum and ceramic capacitors is best, at least one of each and as close the the oscillator as possible. 

Finally don't let the V-Tune pin float. At the very least use a potentiometer between VCC and GND and connect the output of the pot to the V-Tune pin. 

Good luck.