There are already plenty of sites that have a lot of useful information about dating postcards, so rather than rewrite what's already been written I have simply put links to them...
A Brief Guide to Identifying and Dating Postcards in the US (Internet Archive)
Dating Dexter Press Postcards
Dating Frith's postcards to 1940
Dating Guide for Detroit Company Postcards
Greetings from the Smithsonian: A Postcard History
Guide to Dating Curt Teich Postcards (Internet Archive)
Guide to Dating Curt Teich Postcards
Guide to Dating Curt Teich Postcards
Guide to Dating Old Postcards (Internet Archive)
How To Date U.S. Postcards by Postage Amount
Postcard & Greeting Card Museum
Postcard Dating Guide (Internet Archive)
Postmark Dated Curt-Teich Cards (Internet Archive)
Real Photo Postcard Stamp Boxes - How to Identify Real Photo Postcards
Raphael Tuck Postcard Database
Tips for Determining When a U.S. Postcard was Published
Most of the above guides deal with the type of postcard and the various markings and numbering system the manufacturers used, but a rough date can often be determined by the buildings, clothing, vehicles and other items in the postcard picture itself. What people wrote on the back of the card can also provide useful information...
Seventh Street from Wabash Avenue
The text on the front of the postcards says...
Terre Haute, Ind. Looking North in Seventh Street from Wabash Avenue; showing Government Building, Grand Opera House, and Rose Dispensary.
The text on the back of the postcards says...
Printed in Germany
Book Dep't Root Dry Goods Co.
Raphael Tuck & Sons=' Post Card Series No. 2017. "Terre Haute, Ind."
Art Publishers to Their Majesties The King and Queen
This view shows three main buildings, The Post office & Federal Building on the left, behind which is the ornate Rose Dispensary and opposite then on the right, is the Grand Opera House.
The old Post Office stood on the southwest corner of Cherry and Seventh Streets and was built in 1884. It was demolished in 1932 and the site used for a new Federal building. Parts of this old building was used in the Chauncey Rose Memorial that stands in Fairbanks Park.
The Rose Dispensary stood on the northwest corner of Cherry and Seventh Streets and the construction of it started in 1894. Indiana State University purchased it in 1970 and it was demolished in 1972 to be replaced by Oakley Plaza - the North Seventh Street entrance to the ISU campus.
The Grand Opera House stood on the southeast corner of Cherry and Seventh Streets and was opened on November 2nd, 1897. In the 1930's it was converted to a movie theatre and renamed the Grand Theatre. It was demolished in 1960 and the site used by Terre Haute House as a parking lot.
From the dates of the buildings, the photograph used for the postcard must have been taken between 1898, when the Grand Opera house was opened, and 1932, when the old Post Office was demolished.
On the back of the postcard there are other clues to the date of this card...
Back of the Seventh Street from Wabash Avenue postcard
The post card has an undivided back and has the words "Post Card". From December 24, 1901, the Government allowed postcard manufacturers to use the words "Post Card" instead of "Private Mailing Card". The "undivided back" was reserved for the address and one cent domestic postage or two cent foreign postage. From March 1, 1907, manufacturers were allowed to use a divided back, the right side panel was for the address and the left side for writing messages.
So, with a little detective work this card can be dated to somewhere between 1901 and 1907. I have another copy of this postcard that was posted in Terre Haute on June 20th, 1908.
Another example of using a little detective work is the following postcard of Vigo County Fair Grounds...
Vigo County Fair Grounds
This used but unstamped postcard has the text...
The largest county fair in the Wabash Valley held annually at the Vigo county Fair Grounds, south of Terre Haute, Indiana, on U.S. 41. 4-H Fairs, USAC Auto Races, Western Horse Shows, Women's Exhibits, Harness Racing, fine Beef judging and terrific Grandstand Shows are a few of the features to be found at the Vigo County Fair Grounds.
Ektachrome Photo by Kadel
Pub. by Kadel Photographers, Terre Haute, Indiana
Dexter Press Inc.
The back of this card has an interesting story...
Back of the Vigo County Fair Grounds postcard
The first, left hand written text says...
Hope to see you Sunday, June 16th for the U.S.A.C. Sprint Car races at the famous Terre Haute action Track. Hurtibise [sic] will be trying for this 6th straight win.
The right hand written text says...
This was Leonards [the addressee] gift for Father's Day
Ate at Spagetti [sic] Place in Clinton
Using a bit of detective work this card can be dated fairly accurately...
Don Smith was a well-known figure in Terre Haute. He was the chairman of the board of Terre Haute-based First Financial Corporation, a major sponsor of local short-track racing in Indiana. He was also a former promoter of the Terre Haute Action Track and founded the Sumar Racing team with Chapman S. Root which raced from 1953-1960. Jim Hurtubise's NASCAR and USAC racing career spanned the years 1957 to 1977 but his best years seem to have been from 1960 to 1964. June 16th falls on Sunday in certain years, for example, 1957, 1963, 1968, 1974 and 1985. Therefore, I think this card dates from 1963.