The first step in cleaning your dirty coins should be determining what method is likely to be most effective. Understanding your coin type may save you frustration or help you avoid using a technique that may worsen the coin rather than simply clean it.
It is suggested that you should always attempt to clean a dirty coin using the gentlest method available. It is sometimes the case that dirty coins aren't so dirty after all and a simple brushing is enough to reveal all the coin's detail. Using an aggressive method on such a coin would only harm it. Remember that these thin, handmade coins have weathered many centuries and are fragile. Sometimes even a brushing will be enough to break them in half.
When your coin is clean you should attribute it as much as is possible given the remaining detail. While it is not always possible to fully attribute a coin because vital information is worn or missing for some other reason, it is generally the case that you can narrow it down to several likely rulers. Many, if not most, can be at least traced to the emperor who issued it and thus a date range for when the coin was minted is possible to attain. Many more will be fully attributable as to not only emperor but also as to in which city it was minted and sometimes down to the very year it was made.
Once you've attributed your coin as best as you can you will want to preserve it for display or storage. If the coin has not fared well in cleaning you may try restoring a suitably "ancient" look by using one of several re-patina methods available. If you are satisfied with the way the coin looks as is you could give it any of a number of treatments (see "finishing") to keep it looking its best. If you skip this step because the coin looks good enough as it is you may find weeks later that the surface has changed some because the metal had not yet stabilized to its new, clean environment. Sometimes the coin will deteriorate and sometimes it just looks a little duller. Either way, it's worth at least considering a protective layer of some sort.
The final step is choosing a long-term storage method. Many prefer to put their coins in 2x2 flips which can then be written on with the attribution or other information. Others prefer vinyl flips with inserts that carry the information. Doing it this way allows easy retrieval and handling unlike the 2x2's but increases the chances of the coin being misplaced. There are many other ways of storing your coins of course, explore what suits you best!