Inexpensive Mylar-lined cardboard holders can be purchased. The holders have a small, round cut-out for placing the coin so it can be held up and seen from either side. They come in a form sometimes called two-by-two's. They are often 2 inches by 2 inches.
Some holders are sheets that will hold several coins, but each in its own separate area. Others are small, individual sleeves that will hold one coin each. Several styles have holes punched in the edge so that coins can be stored in a binder, but these are not ideal. Coins should be displayed.
Cabinets, ranging from small, glass and wood cigar-box style holders to large, floor-standing Chippendale types, can be bought to hold and show off your collection. The more expensive types are nearly air-tight and some even have archival-style dehumidifiers.
Aged mahogany or rosewood both make excellent wooden cabinets. You should avoid any wooden cabinet, such as oak, that emits organic compounds into the interior. Many types of tree, long after being chopped down and even when not coated with varnish, will produce volatile, organic compounds. Some of those compounds are harmful to coins.
Many collectors, for that reason, will recommend a metal cabinet instead. Several styles exist, some with a coating that helps to prevent scratching and oxidation. Plastic or polystyrene containers are also available, though they rarely display as nicely.
Whichever style of cabinet you get, apart from those with in-built dehumidifiers, it's helpful to have a supply of silica gel packages or other desiccant. They absorb moisture that contributes greatly to oxidation.
Some collectors will coat the coins with vegetable oil or wax before storing, but these practices are controversial. Oil can attract contaminants and wax may give a false sense of security, since it can easily wear off or dull the view. Mineral oil coated would be best bet as it does not deteriorate over long time.
Beyond what to do or use, there are several things to avoid.
Scotch tape or taping coins to cardboard display boards were a common practice, but should be avoided as the glue deteriorates and even the plastic of the tape itself will attack the surface of a coin.
While avoiding exposure to air is good, it's not true that any kind of packaging is better than none. PVC (polyvinyl chloride) sleeves are generally not recommended. They can cause the coin's surface to become coated with a greenish sludge that is harmful and difficult to remove cleanly.
Though displaying coins is preferable, storing them away is sometimes necessary. Paper envelopes can be used for this, but avoid standard office supplies. Get envelopes specifically made for coin storage. The sulfur in ordinary paper can damage coins, especially ones containing copper.
Never store collectible coins in any kind of bulk container, such as penny rolls, plastic tubes, etc. That leads to scratching and denting and doesn't keep out harmful air.
Coins exhibiting corrosion due to impropper storage are oftenly rejected grading by the nations top coin grading services e.g. PCGS and ANACS.
Specially-made sealed containers that hold a collectible are best, though they add to the up-front cost of the coin. In the long-run, however, they will keep your coin in good condition for long term storage and display.