The DFS Logic Flow

Here is the DFS algorithm step by step:

function dfs(u):
    visited[u] = true
    process(u)
    for each neighbor v of u:
        if not visited[v]:
            dfs(v)

Start at vertex $u$. Mark $u$ as visited so you do not come back. Process $u$ (print it, add to result, whatever your problem needs). Loop through all neighbors of $u$. For each neighbor $v$, if $v$ is not visited, recursively call DFS on $v$.

The recursion handles backtracking automatically. When you finish exploring all paths from $v$, the recursive call returns and you continue with the next neighbor.