The question asked in Psalm 119:9 is asked about a young person, but the answer would certainly apply to anyone at any age. The sooner you start the better, but it's never too late.
Psalm 119 is the longest psalm and the longest chapter in the Bible. It is divided into 22 sections, each with eight verses. Each of the sections is represented by a successive letter of the Hebrew alphabet, and each of the verses begins with the letter of that section. Psalm 119:9-16 is the second section and answers the question, “How can a young person maintain a pure life?” The answer is by following God's Word.
God gave us His Word as a gift. In this psalm, as elsewhere in the Bible, God’s word is sometimes also referred to as “law”, “testimonies”, “ways”, “precepts”, “statutes”, “commandments”, “judgements” and “ordinances”, but He did not give it to us to make our lives harder. He gave it to us so that things would go well with us, our days may be prolonged and that we may be blessed. (Deuteronomy 6:1-3)
Its mere existence is not enough however; we must have a part in making it useful in our lives. The psalmist sought the Lord with all his heart, prayed for the Lord’s help to keep His commands (Psalm 119:10), stored up His word (Psalm 119:11), praised the Lord (Psalm 119:12), proclaimed (Psalm 119:13), rejoiced in (Psalm 119:14), meditated on (Psalm 119:15) and delighted in (Psalm 119:16) His word. We need to do more than have a Bible sitting on our bookshelf. We need to read it, meditate on it and apply it to our lives.
Some people get a little confused about meditation because its meaning varies according to context. To meditate on the Word of God is to think about it, mull it over, keep it in our minds. It is a very good practice to memorize it. Then you will have it with you whether you have a Bible with you or not. Jesus didn’t have a scroll with Him when He was tempted in the desert, but He answered the devil by quoting scripture. (Luke 4:1-13) No matter what situation you are in, if you have God’s word in your heart, you will have a source of encouragement, hope and guidance. (Psalm 130:5, Psalm 119:11)
Tips for Memorizing Scripture
(This is my paraphrase of tips given by Robert J. Morgan, author of 100 Bible Verses Everyone Should Know By Heart.)
Choose your verse, decide how long until you want it memorized--a week, three days, whatever--then memorize one word at a time. The first word will be pretty easy. For example, John 3:16, the first word is "For". It won't take you long to memorize that! Then add the second word, the third, etc. Repeat each for however much time you've allowed yourself depending on your goal for completion and keeping in mind that successive words will need more time. The first word might only need a minute. By the time you get to "For this is the way God loved the world", you might need several hours. Keep repeating each section until you have it; then add the next to what you already know. Anyone can memorize anything if they do it one word at a time.