The sauce was likely first created by the chef Collinet, the inventor of puffed potatoes (pommes de terre soufflées), and served at the 1836 opening of Le Pavillon Henri IV, a restaurant at Saint-Germain-en-Laye, not far from Paris. This assumption is supported by the fact that the restaurant was named for Henry IV of France, a gourmet himself, who was born in the Béarn region, a former province now in the department of Pyrénées-Atlantiques, in southwestern France.
A Béarnaise sauce is simply clarified butter, an egg yolk, a shallot, a little tarragon vinegar. It takes years of practice for the result to be perfect. – Fernand Point 
Like Hollandaise sauce, there are several methods for the preparation of Béarnaise sauce. The most common preparation is a bain-marie method where a reduction of vinegar is used to acidulate the yolks. Escoffier calls for a reduction of wine, vinegar, shallots, fresh chervil, fresh tarragon and crushed peppercorns (later strained out), with fresh tarragon and chervil to finish instead of lemon juice. Others are similar. Alternatively, the flavorings may be added to a finished Hollandaise (sans lemon juice). Joy of Cooking describes a blender preparation with the same ingredients. A faux Béarnaise can be produced by adding capers and tarragon to a Hollandaise.
Escoffier, Auguste (1982) [Trans. fm 4th French (Flammarion) ed. 1921]. "Ch. 1: Sauces". La Guide Culinaire [The Complete Guide to the Art of Modern Cookery] (in French). English translation by H.L. Cracknell and R.J. Kaufmann (First American ed.). New York: Mayflower Books. ISBN0-8317-5478-8.