Hi Leila,
I didn't have any luck locating an iFixit-style guide to replacing your battery, but there is a YouTube video that's pretty close to the next best thing.
How to take apart a SONY Walkman NWZ-B183F and change battery - YouTube
The whole process looks pretty well explained and shouldn't be too difficult, but be aware that they didn't quite finish their explanation; as nearly as I can tell, the last step should be to unsolder the old battery from the circuit board and solder the wires from the new battery in. You may have to verify that for yourself, but that's my best guess from what I can see.
Unfortunately, ithe link supplied in the video to buy a new battery doesn't appear to be working. However, it seems they're not hard to find, as that same battery has been used in several different Walkman models. Here's one of the first ones to come up on my admittedly cursory search; I'm sure you can find more with your own search; in addition to AliExpress I'd suggest checking Amazon and eBay.
Battery for Sony Walkman NWZ-B135F NWZ-B152 B173 NWZ-B172F NWZ-B162F B173F B183F NWZ-B142F B-142F NWZ-B143F B153F MP3 MP4 Player - AliExpress 44
As you work, take lots of pictures and once you're done you can use them to create your own iFixit guide for those who come after you with the same problem. It's easy, fun and will garner the appreciation of the repair community.
Create a new Guide - iFixit
Good luck, and let us know how it all turns out!
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