Purchasing a home by itself does not give you any tax relief.
However, if you are getting a mortgage, some of those costs could save you some tax money. You can usually deduct points on a first mortgage when purchasing a new home. So, for example, say you put 10% down and get a $90,000 mortgage to buy your home. Let's say you pay two points on the mortgage. That would cost you $1800. If you itemize your deductions, you could deduct that on your taxes.
In addition, you can deduct any interest paid on the mortgage during the year, as well as any property taxes. This on a $90,000 mortgage at 6%, you would start out paying about $450/month in interest, so if you paid this amount in Oct-Dec. of this year, that would give you around $1350 in deductible costs. In addition, you would probably pay about 1% of the home's value for property taxes. On a $100,000 home, this would be about $1000 per year. If you paid only 1 quarter's taxes in the purchase year, that would be about $250 more you could deduct.
So if we add all that up, the points, mortgage interest and real estate taxes, gives you about $3400 in deductions. If you are in the 15% tax rate, this will increase your tax refund by about $510 (assuming you would have itemized anyway). If you are in the 25% bracket, it would save you about $850.
Going forward, you can deduct your interest and property taxes each year. This would be about $6000 worth of deductions per year based on the assumptions above. So that would save you about $900 per year at the 15% tax rate. Keep in mind that you pay a little less interest each year, so the amount you can deduct each year becomes smaller, but your property taxes will probably go up to compensate.
Of course, your specific savings may vary. Since a standard deduction is $5,350 for a single person, you may be better off taking that rather than itemizing. In that case, buying the house and getting the mortgage would have no effect on your taxes.
I hope this helps!