The name of your coin is 'Winged Liberty Dime,' but most people think Miss Liberty is really the Roman god Mercury, associated with the fleet-footed Greek messenger, Hermes, so they call these coins Mercury Dimes. Your 1936 example catalogs for $1.50 in worn condition. Here is how catalog values of these coins run:
MERCURY DIMES 1916 TO 1931
worn: $5 US dollars approximate catalog value
average circulated: $7
well preserved: $25
fully uncirculated: $100
1916D is the 'killer date' for Mercury dimes. These rarities are worth $100s of dollars, even in well worn condition. If you have one with little or no wear, you're well into in $1000 territory! Be sure the tiny D mint mark is present, and make sure it is not a tiny S. See graphic below for location of the mint mark.
1921 is also a good date for Mercs. If you have a '21D Merc in fully uncirculated condition, you have a $1500 coin; but only about $35 in worn condition.
1926S is another good date and mint mark combination. Catalog value starts around $15 for a well worn piece.
After 1931 the values drop down significantly
MERCURY DIMES 1934 TO 1945
worn: $2 US dollars approximate catalog value
average circulated: $3
well preserved: $5
fully uncirculated: $10
The minimum value for a Merc is based on the amount of silver it contains. Even common dates in poor condition are still valuable due to the silver. Each dime contains 0.072 troy ounces of silver. Go to a precious metal web site, like kitco.com, and find the current value of silver. Multiply by 0.072 and your dime cannot be worth less than that.
There is also an interesting die variety in this series. It is a 1942 over 1941 coin where the 2 and the 1 from the dates appear superimposed. Its value is even greater than the '21D. It must look like our picture. Use a magnifier to see it. Most 1941 dimes do not have the superimposed 2, and most 1942 dimes do not have the superimposed 1.
In the discussion above, please be sure you understand what the weasel word 'catalog' means. Use our Important Terminology page. Also, with the good dates, especially the 1916D and 1921D, it is very easy for a jeweler to glue a D mint mark to a non-mint marked coin, making a counterfiet. All valuable coins should be certified by a reputable certification service. Write to CoinQuest for more information in this area.