Why are my enchantments rubbish, and how do I improve them?

It sounds like your Enchanting skill is too low. Under the Enchanting skill tree, the first perk is called Enchanter. As you spend perk points in Enchanter, it will increase the power of your new enchantments. To get your new enchantments to double in strength, you'll first need to get your enchanting up to 80, spending perk points on the way. Once you have Enchanter at 5/5, your new enchantments will be twice as strong. For example, when I first placed Fortify Archery on an item, it would only fortify it by 8%. Now, and I'm only at 4/5 Enchanter (80% stronger enchantments), when I do the same enchant, it fortifies by 32%.

In addition to Enchanter, you can spend perks in other Enchanting skills such as "Insightful Enchanter" which will increase Skill enchantments on armor by an addition 25%. There are others that will boost your fire/frost/storm enchantments, as well as health/magicka/stamina boosting enchantments, by 25%. These do stack with enchanter for a total of 125% stronger enchantments when Enchanter is 5/5 and the necessary perks are acquired.