1. YOUR GUIDELINES

To start of you need to write down one or more guidelines for you server. This will give your server a solid starting point, and makes everything easier for yourself and your future server members. A guideline is a clear, non-confusing goal for you server, and to give some examples look below. Note that the goals doesn't necessarily has to be obtainable, but it has to give you and your server a shared guideline.

Unclear Guidelines: I want the biggest server in Minecraft!
Clear Guidelines: I want to establish a server around the subject X, because there is no other servers about subject X.

2. TYPE OF SERVERS

Is your server supposed to be a roleplaying, creative, survival, chatting server, vanilla or maybe something completely different? Your server should only have one of these gamemodes available, otherwise you will need multiple worlds inside your server. It is very important that you don't mix-up both creative and survival gamemodes in one world as this would clearly be unfair.
Under this step I would also like to include

Bad Type of Servers: Servers that will give you creative, flying, or other non-obtainable perks if you donate.
Good Type of Servers: Servers which does not have the previously written perks, but instead have multiple worlds for each gamemode.

3. HOSTING OPTIONS

After you've cleared everything up about your server it's time to actually buy a server. Of course you could also run it from home, but that is not recommended as hosting prices aren't that expensive.
You should look for a host with reliable servers that don't have much downtime, preferably over 95% uptime. And isn't to expensive either.
The important part is that you start off with a smaller server, perhaps 20 - 30 players, and then upgrade your server continually. The reason for this is that when you only have 50 players playing on 100 player server, that is both a waste of money, and it will also give you a poor image because those 50 players will think: There used to be up to 100 players, but now there's only 100, this server might not be as good as I thought it would be.

Bad Servers: 30 Active players at peak, hosted on a 80 players server.
Good Servers: 30 Active players at peak, hosted on a 40-50 players server, and upgraded continually.

4. SELECTING YOUR STAFF

This is one of the important steps, as these guys will be your watchkeepers when you're not playing. Of course we've all heard the typical cases of players begging to becomming moderators and that you shouldn't make them moderators because they are unmature. Well, the best moderators are those who you can trust, those who help other players, those who like to chat and be active in the community, those who are not bound by strict rules and dare to make exceptions sometimes.
The best thing you can do is asking those who have been on your server for a long time and do all of the previously written things: helping, talking etc. And not those who you find on the internet and who's never been on your server. Remember that there is no correct number of moderators, but promote them as the server expands to maintain stability and order.

Bad Staff: People "hired" from the internet who's never played on your server. People who are tied to a strict set of rules.
Good Staff: People who's been on your server for a longtime, people who actually writtes in the chat, and responds to other players plea, people who can spell correctly and are mature.

5. RULES

Alongside with your staff you should create your set of rules. Remember your target group, if you make rules like: no swearing, and you're only playing with 15+ year olds, that's not so convenient, give your players some more freedom, everyone likes freedom. At this step your staff should come with good suggestions to your set of rules. There is no correct number of rules, but the more you have, the more unsatisfied players you will have, but then again, you will have more control of you server. I personally would give my players more freedom instead of making the server into a oligarchy. Another good thing is making sure the players actually reads the rules, this could be done by freezing the player in place until she / he reads them.

Bad Set of Rules: Lot's of strict rules that ruins players freedom.
Good Set of Rules: Few loose rules that provides stability on the server, and gives the power to the players.

6. ADVERTISING

As of now you might not be many players on the server, to get some more players on the server you'll need to marketize your server in the community. There are hundreds of places to marketize your server all of where different groups hang out, so sort accordingly to what type of members you want.
Good advertising should be short and clear descriptions of your server, this is also where you want to use your information from step 1. Also remember that graphic eyecandy such as nice banners, posters, youtube videos etc. always is something that the community likes.

Bad Advertisements: Unclear descriptions, no links, no pictures, no videos.
Good Advertisements: All the opposite of the previously written.

7. KEEP IT INTERESTING!

When you have all your server members, and everything is going great, don't let it die out. Let the server stay interesting by hosting various events, the more the merrier. Events could be drop parties, survival games, building buildings together or other types of interactions with your server members. Also remember to frequently add new plugins that will improve the fun of the server, if the players want's some new plugins why not let them? Don't be stubborn and handle all the decisions yourself, let the players choose what they want, sometimes.

Bad Events: There isn't really anything bad about server events, but be sure to notice your server members in good time.
Good Events: Fun events that includes a lot of players, make videos of them and use it for your advertisement for the server.

8. RETAINING MEMBERS

To retain your members, establish a website, it needs to have features such as galleries, forum and events sections. This will make improve relations with your members, and gives them another reason to stay at your server because if they leave, they will most likely leave the forum to, and leaving to things at once is always harder than leaving just a single thing, especially if that one thing is just a server. Also live maps are a very good idea, and I've actually seen servers which let's random people chat with the servers players, this will greatly improve the relations to the community but on the hand, it will also provide more spam, that of course could always be fixed with some plugins.
Official texturepacks are also a great idea because it let's the server's players help each other and thus improving relations. Updating the texturepack could also help keeping the server interesting.

Bad Retaining: No website, no community feel, no choice of sharing your works with the other server members.
Good Retaining: A nice, fancy website with lots of features, use the forum, use the gallery.

9. LAST WORDS

This is the end of my little tutorial on how to run a server properly, I'll be happy to answer any questions you might have, I've run a server before, but I sadly do not run one anymore. Please remember that this is just my opinion on how to run and maintain a server properly.