As with any period, do not feel a compulsion to create a replica of those times. You can, if you feel compelled, but a lot of homeowners just starting out feel intimidated when tackling a style they love. It can also prove to be very expensive to get authentic pieces, even though many are still being made or have been revived due to demand.
Understand the distinguishing features of the style, and find pieces that echo that. Iconic pieces from this era have been adapted and copied endlessly, and chances are that you might be able to find pieces that fit your lifestyle needs and budget, even if you don’t want to spend a fortune on furniture.
Buying vintage furniture is one way to do it, and even if you decide to buy new, generally one large piece can set the tone nicely. Build around it. It does not have to be a set, but in terms of Mid- Century Modern Style avoid too many patterns and stay within a color range, especially for wood.