Standard basis, $(e_n)_{n=1}^{\infty}$ in which $e_n=(\delta_{k,n})_{k=1}^{\infty}$ forms a Schauder basis for $\ell^p, p\in [1,\infty)$.
My proof is as follows:
It is obvious that $e_n \in \ell^p$ for all $n$ since $||e_n||_p=1$. For all $x \in l^p$ we can write $x = (x_1,x_2,x_3,\cdots) = x_1(1,0,0,\cdots)+x_2(0,1,0,\cdots)+ \cdots$. So we can write $x = \sum_{n=1}^{\infty}x_ne_n$ which shows $(e_n)_{n=1}^{\infty}$ is a Schauder basis.
However, I think this proof is so naive and there might be something else to be considered in the proof and I missed it.