The basics: A hashtag is a great way of grouping information together. Just use # directly before a relevant work or phrase (with no spaces). On Twitter it helps show up those words more easily in Twitter Search & you can also follow them on Facebook and Google+. If you click on a hashtagged word in a message, it will show you all other messages with that hashtagged word.
For the basics, read this simple explanation by the Twitter Help Centre.
1. Use a hashtag yourself where it makes sense, like current trends and topics.
2. Use the correct hashtag when joining a discussion or following a particular event/show/conference.
3. Use hashtags to make recommendations like #GreatRead #NowPlaying
4. Use a hashtag to add context or irony to a message, like #fail and #justsaying or make one up to be quirky e.g. #funnythingsoverheardonatrain
5. On a Friday, use #followfriday or #ff to Tweet a message of support to people who you like to follow but PLEASE say why. e.g. “#ff @DotSocialise team, for great blogs on social media” – because it gives people the reason to follow them.
6. Set up your own hashtags, for events or for specific discussions create a Twitter Chat
7. Try not to use more than 2 hashtags in one Tweet or it looks like spam and makes the Tweet difficult to read.
8. It’s not imperative (hashtags aren’t case sensitive) but for ease of reading add capital letters e.g. #PurleyBreakfastClub (refer back to No 4!)
9. If there’s a trending topic relevant to your business/brand use the hashtag in your relevant Tweets to join in.
10. Read up on hashtag fails so you don’t get caught out.
For further reading for getting technical with Hashtags have a look on Hashtags.org