Beleg took the first watch, as Gwindor and Turin slept underneath the birch tree he was perched on. Morgoth wouldn't give up until he has Turin in his grasp, or until Turin dies, whichever came first. But Beleg was determined not to let either of these two things happen. Gwindor's suggestion that they journey to Nargothrond was a prudent one, and one they all agreed to pursue. And so that was the direction they took.
Turin was still rather weak from the days he spent as a prisoner, being dragged by Orcs without break. For this reason, Beleg opted to carry him upon his back, as Gwindor followed silently.
It took them more than a week to reach Nargothrond, and while the guards were somewhat suspicious, they let them pass as a sign of trust towards Gwindor, whom they knew well. In Nargothrond, they were given beds to rest, and clean clothes.
On the second day since they came to Nargothrond, Finduilas, King's daughter, paid them a visit. It was clear that she was there for Gwindor's sake, and Beleg was glad. He didn't want her usurping what was his, after all. Without thinking, he pulled Turin closer and kissed him on the mouth, passionately. After brief hesiation, Turin reciprocated, just as passionately.
And that was the beginning of their new life in Nargothrond.