How can i test a diamond at home?

hit it with a hammer

You can't. It takes sophisticated thermal and optical equipment to distinguish natural diamonds from synthetic diamonds, cubic zirconium or silicon carbide.

Just write up a list of multiple choice questions for it. Maybe some true/false questions too. But don't give it any essay questions. Diamonds aren't really all that intelligent, you know.

I dunno. She if she changes her mind about something(s) she's been refusing to do after you give it to her?!
[seems like a decent 'test'!]
;-)

You can do a hardness test using the Mohs hardness scale.
http://en.wikipedia.org/wiki/Mohs_scale_of_mineral_hardness)
As glass is around a 6 cubic zirconium and diamond are both harder than it, so glass isn't the best test. Cubic zirconium is an 8 while diamond is a 10, so you'd need a 9 to see if you had one or the other on hardness. Most substances that are 9 are used with other substances as composites in body and impact armor, which wouldn't be good for a scratch test even if you even could get a hold of some. But, there is one substance that rates a 9 you might be able to find.
If you have a tungsten carbide drill bit you can try scratching it. If it manages to scratch it, you have yourself a diamond.

If you are really desperate, you can always take a blowtorch to it. Diamonds burn at about 700-900C in atmospheric air at sea level. Cubic Zirconium is 2750C. Your average propane or butane fueled blowtorch is going to cap out at about 1900-2000C. Unless of course you are semi-suicidal (or a very skilled welder) and use an oxygen torch, which reaches a max temp of about 2850C. That will pretty much burn or melt most substances. FYI, this test isn't going to leave you with much diamond left if it turns out to be a legit mineral, just throwing that out there though.

Diamonds are too cold to condensate. Breathe on it.

propose

Bite into it...or maybe not, yeah better not do that actually.

A real diamond can cut glass. It is a sure way to tell.

Diamonds scratch glass, because they are stronger.
Cubic zirconia is almost as hard, but also a bit brighter and almost twice as heavy (1.7 times the weight of a diamond the same size).

A mirror and really good diamond scales should cover it.

You have to have one.