Make sure to have both your singing and instrumental in high quality audio - at least 44.1kHz/16bit (preferably 48kHz/24bit or higher) - WAV or FLAC only.
Try your best to include as many takes of your singing - this heavily shortens the delivery time in case you are not a professional. Make sure your takes are consistent (same style of singing, timing, etc).
Original songs or recreated instrumentals
Everything in the previous section;
Ask your producer to prepare the instrumental and if possible, stems for backup. Also, if possible, ask to remove any limiting done at the master bus (they will know what I mean).
Other details
For fake harmonies, we can take two routes:
Alternative takes: record a few takes of the sections where you want fake harmonies. Pitch is going to be corrected for the harmony. Quieter or more acoustic songs with lots of space for the vocal sound more convincing like this.
Same take harmony: the final take of your singing will be harmonized - sounds less convincing since it originates from a single recording. Dense songs usually work well like this.
Your vocal will always be tuned as best as possible while still sounding natural. The better you are, the better the results.
Make sure you practice before (and not after) sending your recordings.
Make sure that you know proper recording technique:
Avoid clipping your microphone and make sure that your recording sounds as clean as possible.
Do not apply effects or any mixing to the recorded track, unless you are tracking from outboard gear (such as a hardware channel strip).