To add to what has been said (mainly to clarify it), a rough procedure is this.
1. Decide the purpose(s) of renewal. e.g. expiry of passport, change of permanent address, marital status etc.
3. Go through the general checklist of required documents (same page) as well as specific information based on your case in (1). e.g., in case of change of permanent address you would need to provide names & contact details of two local Indian citizens to vouch for your proposed new permanent address. You would also need to mention the nearest police station that would inquire your address.
4. Call them at the dedicated number Yadu mentioned (i.e. 03-7620720 between 2pm to 4pm from Monday to Thursday only ) and check you aren't missing anything. Submit the forms personally at Indian embassy at HaYarkon Street. I think from Tel Aviv Savidor train station you can get 161 to get very close to the address.
Notes:
a. The procedure takes 60 days +/- a week from the starting of submission. Some documents could be provided later on.
b. They would ask your Israeli mobile number primarily to send you the message once your new passport arrives. They wouldnt use email even if you ask for it (or if you don't use your mobile phone often).
c. The passport issuing authority is Indian Embassy in Tel Aviv and this is written on the first page. So if you plan to stay in Arabic countries, factor in that too.
Cheers,