How to Turn Your Old PC to a HTPC
Hardware
First step is to start by checking what you already have available. Assuming that your computer will be a dedicated to playing videos only (unless you want to use it as a game computer also) you don't need a super computer. Any decent computer that can play a high definition movie would be sufficient.
I would suggest you to download a 1080p movie and give it a try, if your can't play a 1080p movie you would need several upgrades. Please note that playing a 1080p movie is pretty demanding, you can also choose to go with a configuration to play 720p movies but I would suggest getting your system ready for all movies.
CPU: A dual core 2GHz or more or a single core 3GHz or more CPU would be sufficient.
Graphics Card: Make sure that you have a digital output in your graphics card, specifically an HDMI or DVI output. If you have DVI instead of HDMI you would need to buy an additional DVI/HDMI converter. If you connect to your computer through DVI output you need to connect your audio separately since DVI only transmits video unlike HDMI which can transmit both audio and video.
RAM: I would suggest using 2 GB or more RAM, if you have less don't worry, it's pretty easy and cheap to upgrade your RAM and it increases your computer performance dramatically. If you are going to buy additional RAMs just remember to check which version you need to buy (DDR2 or DDR3).
HDD: I suggest you to upgrade your HDD as a minimum investment. Most of the old HDDs work with very high noise level, however the new technology HDDs (i.e. WD Green) provide a low noise and energy storage solution. Considering you will have increasing number of movies investing in a new HDD of at least 1 TB space is a sound investment.
Keyboard / Mouse: A Wireless keyboard mouse would be ideal to use as a remote. I use a Logitech K400 which is very cheap and good keyboard/mouse but you can also go for the smaller Lenovo model if you would prefer a smaller controller and not thinking of playing games.
A Quiet System
The real challenge to having a decent HTPC system is having a quiet system. Most of the old computers work like an old diesel engine and that is not what you want to hear while watching your movies.
If you have a noisy computer you may make it silent in couple of easy steps. First step is to check your fans. If your computer is making lot of noise most probably it's coming from the fans. There are several fans in your computer. Usually there is one in front and one in back of the computer case (these fans are usually OEM and make lot of noise) and one in Power Supply (which would make a lot of noise) and one on the CPU and graphics card.
You can try to clean and grease the fans but an OEM fan would start causing trouble in no time so I would suggest changing your fans and your PSU. Check the size of the fans on the case and order new silent fans (which wouldn't cost too much) and also change your PSU with a new low noise and energy green power supply (at least 400W) which is affordable. If you would change your fans and PSU your computer will be quiet and the noise problem would be solved. Once you open your case to change your fans and PSU don't forget to vacuum the dust inside your computer.
Another solution would be ordering a new case. If you have an ugly case I would recommend that solution. A computer case usually arrive with fans and PSU installed, you would need to remove your motherboard and disc drives from your old computer and attach to the new case.
Old HDDs can also be very noisy, the continuous scratching noise would drive you crazy while watching a movie. If you are thinking of upgrading your HDD I would strongly recommend a low energy and noise HDD from WD Green series as I explained above.
Software
Once you have your computer up and running all you need to do is install your new media server. XBMC would be the only program I would recommend. XBMC scans your library and fetches information for your movies and series and you may surf your media with rating from IMDB, posters, plot information, trailers and etc.. You can also include your music library to XBMC or install add-ons to let you play old school emulator games.
Now you have your new HTPC so just enjoy watching your movies.
Notes
I had a 4 year old dual core computer at my house. I didn't need to update my CPU or graphics card, I have updated the RAM from 1Gb to 2 Gb. I had a DVI output which I simply converted to HDMI and connected to TV without any problems. I also purchased a 2TB WD Green HDD. My computer was very noisy and I have seen that the computer case fans and PSU was the main source of the problem. When I replaced those the computer became pretty silent. I am using my computer to play games also and I didn't have any problems so far with the movies or games I played (Civilization V specifically). You can decide to go for a better system with a better CPU, 4GB RAM, a good graphics card and a solid silent computer case, which would cost much more of course. I tried to indicate what is required as a minimum, if you want a better system sky is the limit.
Good Luck with your system, let me know if you would have any questions.