Issue: "I feel like my dialogue is just a wall of 'He said' and 'She said.' How do I change it up?"
Solution: There are several layers to this. Use as many as work for you. Here are a few that I use regularly.
Move things around. You can use the same verb at the beginning of one line and the end of another. (On its own, this isn't much better, and may look off, for instance using 'said' with a question.) He said, "I don't know!" "What do you mean, you don't know?" she said.
Use names. Kermit said, "I don't know!" "What do you mean, you don't know?" Miss Piggy asked.
Use other verbs. Look for synonyms. Scan books you like and make lists of verbs. Think of the meaning you wish to convey with each paragraph to see if it suggests a specific verb. Kermit cried, "I don't know!" "What do you mean, you don't know?" she demanded.
Add adverbs or adverb clauses. I know, some people hate adverbs, but they exist for a reason, and judicious use is good. (I would probably not use them back to back as I do here; I'm just providing multiple examples. Kermit whispered miserably, "I don't know!" "What do you mean, you don't know?" his partner hissed angrily.
Add a pertinent (or trademark) gesture or detail. Kermit stroked the tip of his tongue and sighed, "I don't know!" "What do you mean, you don't know?" Miss Piggy asked with a look of panic.
Refer to the speakers in other ways. The exhausted frog closed his eyes and sighed, "I don't know!" "What do you mean, you don't know?" the pig screamed, simultaneously straightening her wig.
Use combinations of the above, possibly adding something to move the story forward, foreshadow, or set the mood for what comes next. (Yes, I'm exaggerating a bit for effect.) Slumping in his chair, Kermit closed his eyes and sighed miserably, "I don't know!" With every word he turned a grayer shade of green. Her patience wearing thin, Miss Piggy began tapping a hoof on Kermit's Brazilian rosewood desk. "What do you mean, you don't know?" she demanded angrily. With each tap of her hoof, another dent appeared on the desktop. Any other time, Kermit would have slapped the hoof away from his precious desk.
Additional notes:
As always, reading is your friend. If you read widely, you should pick up these and other ideas along the way. If that doesn't happen naturally, spend time in books you love, taking notes of things that you like (see item 3 above.)
If two speakers are alternating speaking in short paragraphs, you needn't reference who is speaking each time, Every four to six paragraphs should be enough.
Stay true to your characters. If Miss Piggy is unflummoxable, don't use words of phrases that show her as flummoxed unless she really is.