Gifts given and received between business partners or employers/employees are treated as income, if they are beyond minimal value.
If your boss gives you a gift, s/he should include it as part of your taxable wages for payroll purposes - which means that some of your wages should be withheld to cover income, social security, and Medicare taxes on it. At the end of the year, the value of the gift should be included in Box 1 (wages) of your form W-2. Assuming that's the case, you don't need to do anything special.
A 1099-MISC would not be appropriate because you are an employee of your boss - so the two of you need to address the full panoply of employment taxes, not just income tax, which would be the result if the payment were reported on 1099-MISC.
If the employer wants to cover the cost to you of the taxes on the gift, they'll need to "gross up" your pay to cover it.
Let's say your employer gives you a gift worth $100, and you're in a 25% tax bracket. Your employer has to give you $125 so that you end up with a gain of $100. But the extra $25 is taxable, too, so your employer will need to add on an extra $6.25 to cover the 25% tax on the $25. But, wait, now we've gotta pay 25% tax on the $6.25, so they add an extra $1.56 to cover that tax. And now they've gotta pay an extra $.39 . . .
The formula to calculate the gross-up amount is:
where [TAX RATE] is the tax rate expressed as a percentage.
So, to get the grossed-up amount for a $100 gift in a 25% bracket, we'd calculate 1/(1-.25), or 1/.75, or 1.333, multiply that by the target gift amount of $100, and end up with $133.33.
The equation is a little uglier if you have to pay state income taxes that are deductible on the federal return but it's a similar principle.
The entire $133.33 would then be reported as income, but the net effect on the employee is that they're $100 richer after taxes.
The "gross-up" idea can be quite complicated if you dig into the details - there are some circumstances where an additional few dollars of income can have an unexpected impact on a tax return, in a fashion not obvious from looking at the tax table.
If the employer doesn't include the gift in Box 1 on the W-2 but you want to pay taxes on it anyway, include the amount in Line 7 on the 1040 as if it had been on a W-2, and fill out form 8919 to calculate the FICA taxes that should have been withheld.