Dialogue is essential to a story and making the dialogue shine is important. Dialogue can be tricky. If you listen to what happens when two friends meet, there's often a lot of chatter that means little or nothing. This doesn't bode well when you're writing a story and two characters meet.
1. Decide what they're going to say that's of importance to the story. There might be a bit of chit-chat but keep it brief. Find a way to get to the meat of why they're meeting. Going round and round just makes the reader want to scream. But sometimes being too blunt can make the reader sit back and say what's going on. So you've revised the dialogue and cut it down to essentials but it still doesn't exactly say what you want to say. What can you do.
2. A little bit of prose can be of help. Show through the character's facial or body just what they're feeling when they're speaking can give the reader a better picture and make what;s being said gains importance.
3. Keep dialogue passages simple. There is nothing wrong with using she said or he said. Even he asked and she answered are great tags. If the dialogue passage is a long one, you don't have to keep identifying the characters after every bit. Five or six exchanges can keep the reader straight as to who is speaking. There's a third way. Using prose to identify the speakers by showing them in action or showing their expressions. This will bring the reader into greater understanding of the story and the characters.