This may take alot of flak but this is a complitation of information that i have gleamed from dozens of articles written by people who can do one finger one arm pull ups.
A hangboard is a potent training tool and can yield unbelievable results when used correctly but can increase the likelihood of tendon injuries hugely.
How to avoid injury on a hangboard as a new climber, any climber for that matter:
1) Do not train dead with dead hangs if you're not in very good physical shape already. The reasoning goes like this. In a dead hang, your muscles are relaxed and your entire body mass is supported by ligaments and tendons that are likely not strong enough to withstand this abuse over time. The solution is to hang with your arms in a combination of bent positions, the most popular seem to be at 90 and 140 degrees.
2) Don't do crimps or any other holds that involve hyper extension of the finger joints. They are extremely demanding on your tendons, especially your B2 tendon and are a sure way to hear that dreaded "pop" as a tendon gives in. There are a few ways to combat this. Train on jugs at first and move to large, flat edges as you feel stronger, slowly progressing to smaller edges as you improve. Train open handed grips, this applies to climbers of all levels. Top climbers often find they are severely lacking in open hand grip strength and are often forced to start training this grip once their tendons decide enough is enough. Apparently, an open handed grip can be just as strong as a crimp in many situations and easier to hold in most cases.
3) Listen to your body!! Its a very fine line between training at your limit and over training. Err on the side of caution and stop if you have any doubts. If it hurts, stop.
4) Your body needs rest after you take part in any training and this is especially true for fingers where they don't recieve much blood and healing takes longer than other area's(think of when you take skin off your finger, how long does it take to heal compared to that same abrasion on your arm or thigh?). Keep in mind that you don't get stronger during your training sessions but rather through resting adequately! When you train hard, your muscle fibers tear fractionally along with tendons and such and they must be given enough time to rest to repair themselves.
I know this doesn't answer any of the questions above but for the sake of completeness, I will include a brief paragraph for those of you with finger tendon injuries. Once your tendons have been injured, there are a few ways of speeding up the healing process and one in particular that your bio-kineticist or doctor won't know about in all probability. It was discovered by doctors working with the US Olympic skating team. They solved Achilles Tendinitis with ice baths. Basically, twice a day they would place the athletes ankle in a bowl filled with ice and water for 15 to 20 minutes, twice a day and the resultant blood rush to the affected area sped up healing to a matter of days. But i must stress that this is extremely painful when done correctly, so you will have to endure the pain if you want results, you will have to deal with it. Another point of warning is that a) leaving the affected limb in the water too long or b) if you have any circulatory problems, you will in all likelihood get frostbite. Consult a doctor before using this extreme method of accelerating tendon healing! PM me if you want more info.
If you still feel you are ready to train on a hangboard, the following workouts seem to be standard issue among the fitness freaks hanging off walls out there.http://www.planetfear.com/articles/Fingerboard_Training__Beginner_1100.htmlhttp://www.planetfear.com/articles/Fingerboard_Training__Advanced_1103.html
I must stress, use your finger board at your own risk! No amount of advice can substitute common sense when training. It is your body and as such, it is unique and will require unique and subtle differences in climbing workouts to be effective and safe. The above is merely a complitation of rule's of thumb I have gleamed from various sources throughout my research into the topic.
I hope this helps