How can we write down a normal form for this following game with information set?
The dimension of the normal form game derived from an extensive form is given by the number of pure strategies each player has.
Generally speaking, the number of pure strategies a player has in an extensive form game equals the product of the number of actions at each information set where she moves. Suppose a player moves at $N$ information sets on a game tree, and at each information set $n$ there are $m_n$ actions, then she has $m_1\times m_2\times\cdots\times m_N$ number of pure strategies.
In your example, $N=2$, $m_1=m_2=2$ for player 1; and $N=1$, $m_1=2$ for player 2. So the normal form game corresponding to your game tree should be a $4\times2$ matrix.
This note describes a step-by-step procedure that's relatively easy to follow.