This is somewhat dangerous to perform with the right equipment, and without the right gear, very dangerous!
Diethyl ether, or CH3CH2-O-CH2CH3, is a great solvent for many things, but is extremely flammable. Professional chemists will be well appraised of the hazards presented in using ether, but the layperson is less likely to be aware of these dangers. Diethyl Ether vapors 'hug' the ground, and in dry air explosive peroxides can form. In other words, even in a spark/flame free environment, explosions can still happen when ether vapour is encountered. For this reason its probably a good idea to have some way of removing vapours from the vicinity (a fume hood would be a fine example) and (Zaphraud suggests) one should not use ether on days with extremely low humidity. Because diethyl ether is so flammable, and prone to ingition, this procedure should be carried out using a hotplater/stirrer designed for use in flammable environments. Such a heater/stirrer does not produce a contact spark when the hotplate is turned on, and generally employs a brushless AC motor for the stirrer, because DC motors with brushes generally produce small sparks which could ignite any stray vapours.
Diethyl ether is prepared from ethanol (a.k.a grain alcohol, ethyl alcohol, drinking alcohol) by heating it with concentrated. The reaction proceeds thru an intermediary, "Ethyl sulfuric acid", as do most reactions of this type.
The reaction is conducted as follows:
Dry (anhydrous) or nearly dry ethyl alcohol is allowed to flow into a mixture of alcohol and sulfuric acid heated to 130°c-140°c. The vapors are collected, and ether and some alcohol and water condense out. The sulfuric acid is a catalyst, but since it becomes more and more dilluted as a consequence of the water produced by the reaction, the process becomes inefficient (which is why anhydrous ethanol is the best!)
The temperature of the reaction should be controlled carefully. At temperatures below 130°c, the reaction is too slow and mostly ethanol will distill. Over 150°c, the ethyl sulfuric acid decomposes, forming ethylene instead of combining with ethanol to form ether.
95% ethanol may be recovered from water + CH3CH2OH pulled from the bottom of the fractioning column (marked 'out')... by connecting it to another column and distilling it...
This may be converted to 100% ethanol by mixing the 95% with calcium oxide and distilling - the water is used up to make Calcium hydroxide! This in turn can be re-fed to the "FEED TANK" after cooling.
Though this is not the most pleasant process, Diethyl Ether may be produced by the condensation of ethanol. To do this, assemble a typical fractional distillation setup with a vigreux column and a three neck flask. Don't forget to drop a stirrer magnet into the flask before clamping everthing up, and you will be heating this on an oil bath (no flames allowed when Ether is around, you know). The vigreux column goes in the central neck, an addition funnel in one side beck, and a thermometer goes in the other side neck.
Add 2x moles (where the x is a multiplier, 1 = 2 moles, 1.5 = 3 moles, etc...) of the azeotrope of Ethanol (ie. 95% ethanol, Everclear) to the flask. Add 2x moles of concentrated (98%) Sulfuric Acid (ie - Instant Power Drain Opener) to the Ethanol slowly (it will heat because of the water). Turn on the stirrer, turn on the heat, and bring the flask up to 130C. Make sure your condenser is well supplied with cold water, and continue heating till the contents of the reaction flask reach 135°C or so.
Once distillation commences, slowly add up to another 2x moles of Ethanol through the addition funnel at a rate equal to the drops coming from the condenser. 2 moles of alcohol (114g) should take 1 hour with a decent vigreux column. A shorter column (or, gasp, no column at all) will require slower distillation (and if you don't use a column, you will have to do some extensive washing of the product with saltwater).
Dump the receiver flask contents into a large beaker or bowl and swirl with 10% Sodium Hydroxide solution until the pH is neutral. Pour this mixture into a separatory funnel to separate the Ether from the aqueous hydroxide and wash twice more with equal volumes of half-saturated Sodium Chloride solution (~18g/100mL of water @ room temp). Let the last wash solution + Ether rest in the flask until everything has settled, then carefully drain off the wash, and pour the Ether out of the top into a round bottom flask. Add 15g of Calcium Chloride (Damp-Rid) for every mole of Ether, drop in stirrer magnet and stir for 2 hours.
Distill the Ether from the Calcium Chloride by heating on a bath (oil or water) at no higher than 45C! Collect distillate that comes over in the range of 31-36°C.