How can you take the Tensor Product in IBM Quantum Experience? For example $$(X|1⟩) \otimes ((X|1⟩)$$
I have tried to look up but couldn’t find anything
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Lets have two general single qubit gates $A$ and $B$. If you apply $A$ on first qubit and $B$ on second qubit, you will get two qubit gate $A \otimes B$. In your case $A = B = X$.
Just note that $X|1\rangle \otimes X|1\rangle = |0\rangle\otimes|0\rangle$.
Here is an example of tensor product $S \otimes T$ implementation:
As tensor product is not commutative operation, $T \otimes S$ is implemented followingly: