The USGA has a handy golf course handicap calculator so you don't have to do the calculation. You can go to the USGA website and find it, or search Google for "course handicap calculator". You will have to know your Index in order to use it.
On January 1, 2020 the USGA moved into the new era of the World Handicap System (WHS). One of the items that changed with the advent of WHS is the formula for calculating a Course Handicap. The USGA says of the Course Handicap:
The Course Handicap calculation converts a Handicap Index to the number of strokes a player requires to play any golf course with a Course Rating and Slope Rating. This allows portability of a player’s Handicap Index wherever they play. The Playing Handicap calculation enables equity amongst players of all handicap levels within different formats of the game. A Playing Handicap is calculated by applying the appropriate handicap allowance to a player’s Course Handicap. For formats of play where a handicap allowance of 100% is adopted, the Playing Handicap will be the same as the Course Handicap.
Course Handicap - For handicap purposes, a Course Handicap is used to determine the number of strokes that a player receives (or gives) on any golf course and for the correct application of net par and net double bogey adjustments.
Playing Handicap - For equity purposes, the Playing Handicap calculation determines the number of strokes each player gives or receives, to ensure that all players can enjoy a fair and equal game when playing with or competing against one another.
The USGA provides a formula with which you first can calculate a number that is the same no matter what course you play. This number is your WHS "Index." Using this Index, you can calculate a second number - your golf "Course Handicap" - for any specific course and tee.
Course Handicap = Handicap Index x Slope Rating / 113 + (Course Rating - Par)
The blue part of the formula is the part of the WHS formula. The portion left of the blue part is the calculation prior to 1/1/2020. For a 9-hole Course Handicap calculation, you would use 1/2 of the Handicap Index in the formula with 9-hole Slope, 9-hole Course Rating and 9-hole par. You can find more in the Rules of Handicapping, Rule 6. Course Handicap and Playing Handicap Calculation, at the USGA website.
As you can see from the formula above and below, the math is the same except for the addition in 2020 of the parenthetical statement where par is subtracted from the Course Rating. Unless you were using the USGA's course handicap calculator, you could use the following formula to calculate your course handicap:
Course Handicap = Handicap Index x Slope Rating / 113
The course handicap was, and still is, really a handicap for a specific set of tees on a specific course or what someone used to call a "playing handicap."
The USGA defined a course handicap in its previous Handicap Manual as...
A "Course Handicap" is the USGA's mark that indicates the number of handicap strokes a player receives from a specific set of tees at the course being played to adjust the player's scoring ability to the level of scratch or zero-handicap golf. For a player with a plus Course Handicap, it is the number of handicap strokes a player gives to adjust the player's scoring ability to the level of scratch or zero-handicap golf. A Course Handicap is determined by applying the player's Handicap Index to a Course Handicap Table or Course Handicap Formula. (See Section 10-4.) A player's Course Handicap is expressed as a whole number. The result of any conditions of the competition, handicap allowance, or competition from a different USGA Course Rating that changes a Course Handicap is considered to be the Course Handicap.
So you had a course handicap that was specific to a set of tees at a certain course as well as an Index that was the same number from course to course. An approved golf club can provide you with a USGA Index which you need in order to calculate your course handicap.