It seems rather basic, but I'm having trouble finding verses that say to read God's Word often. It seems like something that Paul said quite a few times, and it's obviously a good thing, but I can't find any specific verses. Can someone help me?
I don't think there are any verses in the Bible that say "read the Bible", since the Bible as one book is a concept that came after the books were written.
But the following are some of the verses that talk about reading God's word or His teachings.
8 This book of the law shall not depart from your mouth, but you shall meditate on it day and night, so that you may be careful to do according to all that is written in it; for then you will make your way prosperous, and then you will have success. Joshua 1:8 NASB
The Psalms have a lot on meditating on God's law.
1 How blessed is the man who does not walk in the counsel of the wicked, Nor stand in the path of sinners, Nor sit in the seat of scoffers! 2 But his delight is in the law of the LORD, And in His law he meditates day and night. Psalm 1: 1-2 NASB
And of course the famous Psalm 119, I'd suggest you read all of Psalm 119:
12 Blessed are You, O LORD; Teach me Your statutes. 13 With my lips I have told of All the ordinances of Your mouth. 14 I have rejoiced in the way of Your testimonies, As much as in all riches. 15 I will meditate on Your precepts And regard Your ways. 16 I shall delight in Your statutes; I shall not forget Your word. Psalm 119: 12-16 NASB
That's all I can think of for now. But I will update this answer as I remember/find more.