We're talking a long-running series of adventures using the same group of characters, and the same associated players. If this is what you're looking to do with HöL then do read on. You may, however, just be looking to run a simple one-off adventure, in which case I'd recommend you to check out the adventure section. I believe you should read that section before reading this one, anyway. It acts as the basic groundwork for the techniques discussed below. The comments below are vague and generalised, but I hope they will be useful for you. As always, any comments to the usual address. All contributions will be considered seriously.
Why Run a Campaign: All of the following are valid reasons for running a campaign using HöL rather than sticking to shorter single adventures...
Your Big Obstacles: "HöL? Campaign? Ha ha ha ha ha!" For some reason, many gamers don't take HöL seriously. I don't get it. Your biggest problem, though, is keeping up interest. Don't decide to run a campaign arbitrarily - you need strong ideas to keep a campaign going. Non-stop action is hard to maintain over long periods of time. The advantage is that character development becomes more important, opening up doors that players might never have previously considered. Also you need to keep the gaming group of players together, running regular sessions (disjointed sessions lead to a lack of interest and forgetting recent game events) with hopefully the full group. This problem exists for any gaming group involved in an RPG campaign. If you're playing HöL you should be experienced gamers, so this should be something you can work around.
Consider your Setting: Will you restrict the characters to HöL or explore the COW? You could begin your campaign outwith of HöL for a while, and then drop them in it. This could let them build their characters up a bit, allowing them to survive (marginally) longer on the hellhole. Alternatively, you could restrict all gameplay to HöL itself, since there is enough background given in the books to keep you going a while. What I feel is the most interesting scenario is "Escape from HöL" where the group must work towards the goal of escaping the planet (this should require a starship somewhere in the equation) and if they play well enough, they can be rewarded with further adventures amongst the other planets of the COW - a near infinity of possibilities awaits them.
Campaign Goals: Over extended campaigns, many goals can be in force, and completing one goal often leads to a new one springing up. It is important for players to have definite goals that they can feel they are working towards. The players' goals may not necessarily be the ultimate ends to which you push them, of course. If the group has no focus, they may well feel that they are just stumbling along while you have your fun. Over an extended campaign, this will lose you players. Don't be afraid to throw sub-plots and side adventures at them, but do keep to some main storyline as well. The best stories can be described simply. And remember that your goal is no longer to kill them all.
Choosing Characters: You have to be more responsible with your character creation for a campaign. Unbalanced characters cause minimal damage in a short adventure, but in a campaign they can wreak havoc. Keep in mind that the characters will increase in ability over time, so don't start them off with huge powers. You appreciate more that which you have worked for. It doesn't matter so much to give players a great deal of intial control over character creation, since they will instead be able to control their characters' growth. In a way, they will ultimately have more power over the characters than you do.
A Plea: I would like to reinforce my previous sentiments by saying that you must have ideas to run a good campaign. Players should be happy with you, with their characters, and with each other, since you're going to be together for a while. This is a commitment, but it must always be fun as well. HöL is fun, and your games should reflect this. But deal with foolish players accordingly - don't let them spoil everyone else's fun.
An Example: There is little point to me giving you an example of a campaign since it becomes a very personal thing to run. The ideas behind it must be a part of you, so that you can feel how it moves and changes. I have personally held plans for many years now for running a campaign based around a mysterious woman called Pandora and three starships (the Prometheus, the Epimetheus, the Atlas) but I've never got a group of players that I think would be committed to it. If you really want to use this for your campaign, then I'll provide more details on request.