how is this new value determined?
According to Publication 551:
The basis of property inherited from a decedent is generally one of
The FMV of the property at the date of the individual's death.
The FMV on the alternate valuation date if the personal representative for the estate chooses to use alternate valuation. For
information on the alternate valuation date, see the Instructions for
The value under the special-use valuation method for real property used in farming or a closely held business if chosen for estate tax
purposes. This method is discussed later.
- The decedent's adjusted basis in land to the extent of the value excluded from the decedent's taxable estate as a qualified
conservation easement. For information on a qualified conservation
easement, see the Instructions for Form 706.
FMV is Fair Market Value - which is the price that a willing buyer would pay for the property with reasonable knowledge of all the facts of the property.
The rest generally apply to farmland or other special-purpose land where the amount of income it generates is not properly reflected in the market value.
One or more real estate professionals will run "comps" that show you recent sales in the same area for similar houses to get a rough estimate of fair market value.
Does it go off of the tax appraised value?
Tax assessment may or may not be accurate depending on tax laws (e.g. limits to tax increases) and consistency with the actual market.
Should you, prior to your death, get an independent appraiser to appraise the value of the property and include that assessment of the properties value with the will or something?
That should not be necessary - another appraisal will likely be done as part of the estate process after death. One reason you might do one is if you are distributing different assets to different heirs, and you want to make sure that the estate is divided equitably.