How do I know if a transformer will output A.C. Or DC?
I think you have been led astray by terminology. As others have noted, a transformer converts one AC voltage to another AC voltage level, while providing some electrical isolation. In your case, it converts 230V Ac to 7.3V AC.
What you may have been thinking of is a small power supply that sits in a plastic container and plugs straight into a wall. Some people call these "wall warts" and some call them... "transformers". Yes, they CONTAIN a transformer, but they also have rectifiers and (in the better ones) voltage regulators to give you a nice steady DC voltage.
If you want DC, add a good power diode to one of the output pins, then place a capacitor across the result. If you use a big capacitor, they have a polarity marking.
WARNING: You are now playing with circuitry powered by mains electricity! While 7.3V sounds tame, you have a 230V input, and that is DANGEROUS.
With that in mind:
Buy A Multimeter A decent one will have AC and DC voltage ranges. In fact, having one means you would have been able to answer your own question (AC or DC voltage present).
UNPLUG your stuff from mains if you can - it's a basic safety precaution. Put everything in an enclosure, to keep out curious children / pets / etc. 
Electronic goods can be fun, but the mains isn't really the best place to start. You're trying to power something else - a chip and a relay. Whatever they do, you should be focusing more on that, than on mains power supplies as an introduction to electronic goods.
Maybe you know all about safety already. However, none of the other answers I saw addressed this point, and it's really not something we should "assume" everyone "just knows".