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ZXDS is an emulator of Sinclair ZX Spectrum for Nintendo DS, written by Patrik Rak.
It accurately emulates Spectrum 48k, 128k, 2/ 2A/ 3, and Pentagon, and supports SNA/Z80/SZX snapshots, TAP/TZX/PZX tape files, TRD/SCL/DSK disk files and RZX replay files.
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It has some other noteworthy features, like the ability to download all these files online over Wi Fi, peer-to-peer Wi Fi multiplayer, or Kempston mouse emulation.
It is available entirely for free, however donations are a nice way of saying "Thank You! Just download the archive using the link below, unpack it and copy only the entire directory (not just its content, but the directory itself) to the root of whatever device you use to run homebrew on your DS (or any other compatible model, like DSi or 3DS).
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Make sure that even the empty subdirectories are copied properly (in particular, make sure the to elsewhere on the card, like to the root itself, to make it more accessible.
Other directories in the archive contain optional extras, so check the README files in each and install to the right place only those files which you really want.