There are a myriad of ways one can determine an approximate (or sometimes an exact) date for your old postcard. 

Among them are:

1. Look for the Obvious, First.

2. Postcard Styles

3. The Number of Stars on US Flags

4. ZIP Codes, Postal Zones & Postal Rates

5. Theatre Marquees and Billboards

6. Cars, Clothing Style and Architecture

7. Publishers

8. Do the Tough Stuff, Last.

Here are the details:

Look for the Obvious, First.

Some postcards, especially chromes printed by the LL Cook Company and a few others, and many vintage postcards by the Detroit Publishing Company (aka known as Detroit Photographic or Phostints) put copyright dates right on the card (about 1898-1907). These later dates usually applied to the image and in many cases the card was actually printed a few years later.

Some postcards are either explicitly dated by the sender or implicity dated by mentioning the current president or even a disaster or other current event mentioned. I found a William Jennings Bryan poster in the window of one real photo of a house once.  I've seen other campaign headquarters signs for local politicians or a couple of times for the Bull Moose Party.

 

Postcard Styles

Older cards without a line or divider on the address side, date between 1901-1907.  Leather cards are usually from about 1901-1904.  Older cards with a white border date usually between 1914-1918 (unless they are linen).  This saved on ink costs during WWI.  Linen cards generally date between 1930-1950.  They have a woven texture.  Chromes are after 1940, but mostly from the 1950s-1960s.  Larger Continental cards (about 4 x 6") date from the late 1960s to the present.  Litho cards are cards that are all one color (usually tan, but also red, blue, green, etc.) and they date from the 1920s-1940s.

The Number of Stars on US Flags

It is possible to date the image of your postcard if the US Flag is completely visible. A 50-Star Flag dates the card later than 1960. A 49-Star flag was only used for one year, dating the postcard to 1959-1960. The 48-Star flag flew for about 47 years (1912-1959) so that's not so helpful, except for cards on either end of those dates. The 46-Star Flag was flown from 1908-1912. The last one for our purposes would be the 1945-Star Flag which was the official flag from 1896-1908.  Oklahoma, Hawaii and Alaska cards can also be dated depending on the information or postmark as they became states after the postcard era began.

ZIP Codes, Postal Zones & Postal Rates

Before every little post office in America was given a ZIP Code, big cities were given a postal code. This lasted from 1948-1964. Any card with a code was almost assuredly from this era. Therefore, any address on a vintage postcard from a big city without a Postal Code or ZIP Code is probably before 1948. I say probably because perhaps not all publishers followed the "rules". Any small town address without a ZIP Code probably dates before 1964, any with a ZIP Code most assuredly is 1964 or later.

If your card is from after 1952, the cost of the stamp may help you date the card. Remember, though, that the card may have been produced many years before the stamp was placed. On rare occasions, the current stamp rate is printed on the back of the card giving you the probable date of production. People often think penny postcards are very, very old, but the once-cent stamp was used for virtually all years up until 1952 (with one or two brief exceptions).

Theatre Marquees and Billboards

If you can make out a particular movie showing at a theatre you can usually date the card by when the movie was released. Only on rare occasions would a re-release throw you. Sometimes billboards and signs may advertise a 1957 Chevrolet or announce the 1938 County Fair.

Cars, Clothing Style and Architecture

If you know even a little about cars that can help you date the cards, at least within a 5-10 year period. Of course, the Volkswagen beetle didn't change much between the 1940s and 70s so that won't help too much ("The More Things Change, the More They Stay the Same").  Occasionally, you may even be able to read the year on license plate!

Clothing or hair styles can also be used. Flapper hair-styles were only popular for about four years (1923-1928). The Bee-Hive was popular from about 1963-1967.  Bell-Bottoms probably date your card to the 1970s. Leisure suits were in fashion during the late 1970s. Most men wore suits and hats in public until well into the 1960s. 

Decor - Art Deco buildings (lots of bus stations were built with the block style windows and rounded corners of the era) were mostly built in the late 1930s, early 1940s. Interiors - Red Carpet, Walls, and Everything else were the rage in the 1950s until Mod Decor (Flower Power, etc.) started in the late 1960s through the early 1970s.

Publishers

Almost all Curteich Company postcards have numbers either on the back middle, front lower right or stamp box (newer cards).  You can find the corresponding dates by looking for a charts published by Refried Jeans or the Lake County Forest Preserves.  Search for "Curt Teich Postcard Archives".  Other companies may have this information listed as well. Wayne Publishing's silver border series date to the 1940s.

Do the Tough Stuff, Last.

Depending on how important the exact date is, you could do lots more research on the internet. The building or destruction dates of a particular building could give you some paramaters for your card. The same could be said for the particular photographer. Perhaps a phone call to the current business owner could help - often motel roadside postcards have the address right on the card. I once located the current owner of a home depicted on a real photo postcard by seeing the doctor's name on a sign in front of the house!

You may also find the dates of vintage postcards by by going to one of the genealogy websites and doing reseach about the person who sent or received the the card.