Let $C$ be an embedded circle in $\mathbb R^n$. Then any trivialization induces a stable framing of the normal bundle $\nu(C)$ of $C$ in $\mathbb R^n$ in the following way: $$ TL \oplus \nu(C) \cong \underline{\mathbb R}^n|_C $$ and on the other hand we have $$ TL\oplus\nu(C) \cong \underline{\mathbb R}^1 \oplus\nu(C) $$ from the trivialization of $TL$. Hence this gives an isomorphism $$ \underline{\mathbb R}^1\oplus \nu(C) = \underline{\mathbb R}^n|_C $$ which corresponds to a stable framing.
How do I have to choose the circles $C$ such that I obtain the two elements of the stable framed bordism group $\Omega_1^{\textrm{fr}}$?
See Figure 2 (page 8) in this introduction to the Kervaire invariant problem by Hill-Hopkins-Ravenel. A similar picture is also in Hopkins' slides from the Atiyah80 conference.
Essentially, an example of the trivial framing is the embedding of the unit circle inside $\mathbb{R}^2$, and an example of the nontrivial framing is given by the embedding the circle as a "figure eight" in $\mathbb{R}^3$.