An Oleh is considered to be an Israeli citizen from their date of Aliyah.
An Oleh from a country which does not allow dual citizenship has a 90 day period following date of Aliyah during which they may decline Israeli citizenship.
How does a person decline Israeli citizenship?
By filling out an "ARLI" form at their local branch of Misrad Hapnim within 90 days of their date of receiving Oleh status.
Why would a person decline Israeli citizenship?
Generally because they are a citizen of a country where dual citizenship is not allowed.
Travelling abroad subsequent to Aliyah
An Oleh can enter and exit Israel using their foreign passport for 90 days following their date of Aliyah.
90 days after receiving Aliyah status, an Oleh is required to travel with a Teudat Ma'avar (Temporary Passport / Laissez Passer) or an Israeli passport in order to exit the country. Passports and Teudot Ma'avar (Temporary Passports) are issued by Israel's Interior Ministry.
Israel is currently introducing biometric travel documents. More information is available on the website of the Interior Ministry.
New immigrants may apply for an Israeli passport for travel outside of Israel starting 90 days after their Aliyah (immigration to Israel) date. Israeli passports are issued by Israel's Interior Ministry.