You can't find "the steps it takes" because that's a random quantity. But you can find the expected number of steps it takes, starting in a given state.
In your example, let $u_1$ and $u_2$ be the expected number of steps until reaching the absorbing state, starting in states $1$ and $2$ respectively.
Suppose, for example, you start in state $1$.
The first column of the matrix says that after the first step, with probability $0.3$ you stay in state $1$ (and then the expected number of additional steps until reaching the absorbing state is again $u_1$); with probability $0.6$ you are in state $2$ (and then the expected number of additional steps is $u_2$), and with probability $0.1$ you are in the absorbing state $3$ so no additional steps are needed.
This says $u_1 = 1 + 0.3 u_1 + 0.6 u_2$. Do a similar analysis for starting
in state $2$, getting another equation, and solve the system of two equations
for $u_1$ and $u_2$.