If you are ready to start studying your Bible instead of just reading it devotionally (reading devotionally is good, too, but in my experience study opens up whole new worlds) here are a few tips and ideas I have. Of course, these are not the only ways to study the Bible, but they are what I have done personally. You will need a Bible, preferably one with cross references; a concordance; a notebook; and a pencil or pen. Also helpful is access to different version of the Bible. Bible Gateway is a good site for different versions, and I'm sure that there are online concordances available (if you know of a good one, please let me know.) I generally either start with a particular verse or passage that I want to study OR a topic (e.g. widows, hope, etc.)
If you start with a verse:
• Look it up in different versions
• Look at the marginal notes (especially other scripture references)
• Look up key words in the dictionary (even words you know the meaning of)
• Look in a concordance for the Hebrew or Greek meaning of the key words
• If you find a word that you want to investigate further, see below
If you start with a topic:
• Look up that word in a concordance to find verses that speak to you (this can be tricky, especially if the topic is huge, hopefully I'll write more about this step later)
• Look up other related words (you can find other words translated from the same Hebrew or Greek word in a concordance or you can get ideas in a thesaurus)
• If you find a verse to investigate further, see above
If a topic is too big or overwhelming or is just not what you are focusing on right now, but you would like to get to it later, start a collection of references, gathered as you come across them. Save them for later when you are ready to do something with them.
I would encourage you to write out verses by hand, as much as is practical. This is very helpful to paying attention to every word and really meditating on it. Sometimes it is good to write a verse on an index card and put it where you will see it frequently. Sometimes I end up writing the same verses down multiple times over a period of weeks or months, and getting something new out of them every single time. Of course, the most important elements are an open heart and a willingness to listen to God’s leading and the Holy Spirit's insight.