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Nandhini GovindrajNandhini Govindraj 

How the user can edit the record but other users can read access only

SwethaSwetha (Salesforce Developers) 
HI Nandini,
You can do a manual share of records. Manual sharing lets record owners give read and edit permissions to users who might not have access to the record any other way.

See related info :

If this information helps, please mark the answer as best. Thank you
The TechieThe Techie

Make OWD setting Private for that object and with sharing setting provide access to other users.