The most important thing to remember about hops is freshness. There are innumerable different hop varieties and personal preference is the rule here, except when attempting to duplicate a style or specific commercial brew. I am in the habit of making recipes on the fly and using whatever I can get my hands on, keeping hop varieties in bulk that I like best. Get to know hops and spend time in breweries where they may allow for a home brewer to smell the fresh hops they use in their brews.
A rule of thumb for beer styles, is that German brews are primarily made using German Noble hops (Tettnanger, Hallertau, Spalt, Saaz) and traditional British ales are made using English Noble hops (Fuggle, Golding, East Kent Golding). American brews can be made with anything, and being a hombrewer, rules are meant to be broken.
One key thing that I have found, is that hop pellets bought in bulk tend to be fresher (as they have been handled less) than hops bought in 1 oz packets, so it is something to keep in mind. I often buy a pound of hops and store them in a glass jar in the freezer and they keep nicely. I have also found whole fresh hops are supierior, but are a little bit difficult to handle as whole hops take up more space in the brew kettle, reducing yield. Remember, if any brewery is offering hops for sale, jump at the opportunity. These hops, whole or pelletized, are almost guaranteed to be the freshest hops anywhere short of growing your own.
Hops are something to be experimented with and they can be added at every step of the brewing process with different effect. The alpha acid percent associated with the hop is the weight of humilones (the alpha acids) in dry weight in relation to the rest of the hop. Bitterness comes from boiling hops in the wort for an extended time. There are calculations for added hop bitterness that can be done based on any lenght of time, from 5 minutes (considered negligible) to as long as 90 minutes or more. At some point of time, maximum bitterness utilization is achieved, usually around 90 minutes. Flavor and aroma come from hops added the last 20 minutes or so until the end of the boil and flame off. Aroma is best from hops added at the very end, or even in the secondary. It must be noted that hop character will decrease with the fermentation, so if a high flavor and aroma brew is desired, large quantities of hops are needed, It is assumed that hops are sanitary, but this is not 100% true. There can be bacterial strains present in rare instances that will turn beer sour where hops were added unsanitized. This is the call of the brewer as to the amount of risk taken. Keep in mind that alpha acids will create the skunky aroma and flavor when exposed to light, and it happens very quickly. Keep your clear and green bottles in the dark, and use a beer stein to protect your beer when out in the sun!
Hops also contain beta acids, or lupulones. Beta acids have little value in the initial brewing process. They do however, produce bitterness when oxidized. This means that as a beer ages, the alpha acids oxidize (and they dont produce bitterness when oxidized) bitterness is lost, but if high beta acid hops were used, this can replace some or all of the bitterness lost. Beta acids are also responsible for the cheesy aroma of old (and oxidized) hops. This is similar to the aroma of aged cheeses such as parmesan and romano. If you smell your hops and start craving your favorite italian dish, well then you have identified a problem!
Hops also contain essential oils that make up 1 to 1.5 % of the hop's dry weight. The most important of these are Terpenes. These are volatile compounds that provide aroma, and will boil out of wort. Terpenes are not only present in hops, but are responsible for the aroma of fruits, flowers, herbs, and other plants. Aroma Terpenes can be retained by adding at the very end of the boil or steeped at flame-off. Terpenes stabilize when oxidized retaining hop aroma when a finished product ages. Of course, these oils are not mentioned on hop packaging in homebrew shops. The aromas of typical hops include citrussy, grapefruit, piney, lemon, resinous, cedary, rose petal, etc.
I have added hops at bottling time to the boiled malt extract priming sugar (flame off) with some success, dumping this through a strainer to remove the larger hop chunks. The hot priming sugar sanitizes the hops, and adds the hop character, without making a sacrifice of beer quantity (beer is lost to the hops placed in the secondary or wherever).
I have added hops to the mash (mash-hopping) and have loved the results, though it may not be what a hop head wants in a beer. Mash hopping takes the finishing hops from the end of the boil and adds them to the mash. The flavors are more rounded, but seem to not be diminished by fermentation. More thoughts and notes on this will be added to the site in the advanced section, and as more experimentation is complete.
Of course any homebrewer is going to hear about "dry hopping". As I had mentioned above, this is the brewer's call, but it is an effective way to add hop character to a beer. Adding hops to the secondary after fermentation and prior to bottling (or kegging). Another method for sanitizing these hops is to place them in a strainer and boil water below the strainer for 15 minutes or so. Either way, adding hops to the secondary is frequently used by the pros. There are recipes in the Papazian book that use this technique. If the beer is being kegged, hops may also be added to the keg.
Another advanced technique is to first-wort hop. This is for all grain brewing, and hops would be added to the brew kettle while the wort is being collected in the kettle. The hops added is a portion of the bittering hops. The aroma and flavor compounds are extracted and bonded to the proteins as in mash hopping, then the alpha acids are extracted for bitterness in the boil.
Keep in mind that if low alpha acid hops are used to provide bitterness in the boil, some grassy flavors may be imparted on the beer, as more hops are required for bittering, and hop leaves have grassy flavors that are noticeable when large quanities are used.
For those with the space, patience, and proper soil, it is also an option to grow hops. Hop risomes are available from many homebrew shops. I tried this once, but my soil is not very good. I obtained some growth by year two (it takes at least a second season before the plant produces any hops, and more than that for a decent crop), but then my rig was destroyed by a tropical storm. Home grown hops are best used for flavor and aroma as the only way to determine the alpha acid level of the hops is to have some sent to a lab. Do some research and give hop growing a try. Fellow home brewers are always interested in home grown hops!