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\begin{array}{l}\phantom{11)}\phantom{1}\\11\overline{)99}\\\end{array}
Use the 1^{st} digit 9 from dividend 99
\begin{array}{l}\phantom{11)}0\phantom{2}\\11\overline{)99}\\\end{array}
Since 9 is less than 11, use the next digit 9 from dividend 99 and add 0 to the quotient
\begin{array}{l}\phantom{11)}0\phantom{3}\\11\overline{)99}\\\end{array}
Use the 2^{nd} digit 9 from dividend 99
\begin{array}{l}\phantom{11)}09\phantom{4}\\11\overline{)99}\\\phantom{11)}\underline{\phantom{}99\phantom{}}\\\phantom{11)99}0\\\end{array}
Find closest multiple of 11 to 99. We see that 9 \times 11 = 99 is the nearest. Now subtract 99 from 99 to get reminder 0. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }0
Since 0 is less than 11, stop the division. The reminder is 0. The topmost line 09 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.