I'm in the position of inheriting a number of small (between 5 to 20 hr) jobs which largely involve providing fixes and changes to existing systems on a contract basis. I've never done the self-contracting thing before - all my previous wages were set by the customer / employer.
How do I decide how much to charge? I don't want to under-value myself, but I also don't want to scare the clients away.
Edit in response to close votes: Sorry, I forgot to add "As a programmer" to the title. =)
A good rule of thumb is to figure out how much you'd get paid in salary to do that if that were your job, and charge 2x to 3x for short-term work.
For example, if you would make $90,000pa, you'd charge $90 - $135 per hour.
That may sound like a lot but there are lots of reasons for this. Salaries have lots of stuff inbuilt like (some) security about hours, insurances (health, unemployment, professional indemnity, public liability, etc), sick leave, maternity leave, annual leave, long service leave (depending on your country), bonuses, provision of equipment and work space (where you might otherwise have to provide your own), pension/retirement funding, allowances (car, phone, laptop, etc), status, respect from coworkers, etc.
These things need to be factored in when pricing your services. Any reasonable employer will realize that casual employment is more expensive than full time employment because the employer only needs your services for possibly a day so you (instead of the employer) are wearing the risk and paying the costs.
You need to determine what you are worth and then balance that with how long it would take you to do the job compared to the average guy that can also do the job. If it takes me 1 hour to do something at $100/hr and it is going to take you 4 hours to do the same job...I am not saying to bill yourself out at $25/hr...but use this formula to be aware of where you are in life!
Next...when possible use the escrow services of sites such as getafreelancer.com, scriptlance.com, guru.com, or elance.com (this being the most professional of these sites). RentACoder.com may also be of use to you.
Keep records of everything.
Write as much down as you can in the form of an agreement up front and not only specify what you WILL do but just as important is that you specify what you WON'T be doing. This last part is important in being clear instead of assuming on both parties parts that you both understand what is being agreed too.
When determining your price consider things such as benefits (you pay for them), taxes (you pay for them...save 40% just in case...pay them quarterly so you know where you are and don't get surprised at the end of the year), etc.
This is such a tricky question, you have to build in a lot of stuff when you think about the rate, very short contracts (20 hours) are fiendish and usually best avoided.
Remember you will little to no flexibility to re-negotiate rates with the same company, if your rate is too low, it will most likely stay that way, even for subsequent contracts.
As to how much to charge, for very short contracts I would probably charge about double my "normal" contracting rate, and I would ensure the scope is well defined.
Don't be afraid to charge more than what you think you should, there are tons of hidden personal costs that you just forget to factor in.
Personally I like to vary my charges depending on the type of project and the buyer. If I'm doing contract work for a big corporation, I'll charge more than for a small business. If the job involves complicated niche services, I'll charge more than I would for simpler stuff. If I'm likely to get a lot of repeat business, I'll charge a little less to get my foot in the door.
I tend to like to rate jobs based on the value of the job itself, rather than some hourly rate. As long as you are careful with your contracts and don't give away too much of the ownership to your code, you can get a lot of re-usability out of code you've already written, and there's no reason for you to give that code away to new customers for free.
balance whatever the market will bear vs. your opportunity costs
for example, if the work is interesting and you're bored, you might be willing to do it for free; on the other hand if the customer is in dire need and has no where else to turn to, they might be willing to pay thousands of dollars to get the job done
somewhere in between these two extremes is a number both of you can be happy with