Nothing may be more symbolic of the idea of immediate gratification than a cup of coffee from a French Press. All you do is put the grounds in, pour in boiling water, pop the top on and push slowly. Presto! Finished freshly brewed coffee without the wait for a coffee maker or percolator. You can buy the size press you need to have just as many cups of coffee as you want. The only problem is that we tend to leave the grounds sitting in the tank until we get home in the evening. During the day, the oils soak into all of the parts of the press until it's shiny innards are a dingy mess.
Rinse off the metal screen assembly on the end of the plunger in water as hot as possible whenever you use your press. Wash the glass carafe (or beaker), either in hot, soapy water or hot water and white vinegar. Unlike coffee pots and makers, soap can be used inside press beakers since there are no nooks, crannies or surfaces where the soap can stick to ruin the taste of future brews. Rinse everything well before the next use.
Take your press apart periodically to get the coffee oil out of the mechanism that actually compresses the coffee. The assembly at the bottom of the plunger consists of the press itself (with holes and a spring around the edge to slide in the beaker), a screen, to keep the grounds from floating around the finished brew and a frame to stiffen the whole thing so it doesn't flop around as it's pressed down. Most compression assemblies can be taken apart to clean the whole surface of each piece. You can soak these pieces in white vinegar or scrub them with baking soda to remove the oil that settles between layers.
Let vinegar and baking soda "boil " away the oil as a more aggressive method of cleaning the compression assembly. Pour in enough vinegar to cover the assembly as it sits at the bottom of the beaker and add a spoonful of baking soda. Replace the plunger instantly and move it up and down as the vinegar and soda interact. Since this can pit the metal or ruin a plated finish, be sure to know what your assembly is made of and use this method only for serious staining. Rinse carefully in hot water and vinegar before using again.
Be sure that the compression assembly is rinsed clean and dried before re-assembling. Dry all pieces carefully with a soft cloth and reassemble all the pieces in the proper order. If the frame and top are chrome or some other shiny metal, be sure to dry and buff to keep the press looking sharp and remove any liquid that might stain or corrode.