DPHunter and Troggy - you have gotten some excellent advice from these responses and you both should 'have at it'.
I've been reloading for just about 40 years and if you are shooting calibers that are not sold in bulk quanities like mil-surp or target (38 spl, 9mm, 45acp, etc.) you will need to think about reloading for both the economy of scale and the incredible amount of satisfaction you get when you have properly taken game with your own handloads.
The advice is accurate - check with your local gunshops for reloading manuals, equipment and supplies. Purchase a good reloading manual that carries reloading data on your preferred cartridges and check out the Reloading Forum further on down the list of forums here at Graybeards. When you feel you are about ready to 'get into it' check with some of the other members on your load preferences and see what those with experience with those calibers suggest. Then you can have fun.
Rules of thumb - do not allow distractions while you are reloading - this includes wife, girlfriend, telephone, pets, children, smoking, etc., as distractions are a known basis for reloading errors and the possibility of very serious problems for both the shooter and the firearms involved. Pay very serious attention to what you are doing - if you handload for dangerous game you are wading in dangerous waters and you need to be attentive to your reloading activities.
Start with the basics - a good single stage press like an old RCBS Rock Chucker or an older Lyman single stange press is the best place to start.
There are many good manuals out there but I like the Lyman Pistol and Revolver Handbook, it is pretty comprehensive. There are others that are also well written and have good reloading data. In each you may find some differences betwixt powder charges and velocities, etc.,etc., but don't let that sway you. Stay within the prarameters of the load data provided and you should be safe.
You won't need to load for max velocity with some of these calibers and milder loads have and will continue to work just as well as heftier loads do. Accurate shooting is a lot of fun and quite satisfying. Good luck. HTH. Mikey.