The most important tip - always look how many troops a province can support and never hire more than that - they will die out really quick until they reach the approprite number, that depends on province's population and fortress's size. Having a good commander always helps. It is a good idea to storm fortresses if you are stronger - enemy provinces support a limited number of enemy troops (once the province becomes yours, this number increases significantly) and you will loose a lot of people during the siege.
Always balance out infantry, cavalry and artillery. Artillery is the most attrition-resistant, infantry - the least. Make sure you have a lot of infanry before going to war. It is essential for storming fortresses. In addition, armies that only have artillery are very vulnerable - even a small enemy regiment can make it flee.
If you have more specific questions, I will be glad to help.