OpenGL expects matrices to be specified as a one dimensional array of float values in column major order. Jogl gives you the choice of passing this array either as a float/double array or as a Float/DoubleBuffer. In code this translates to
Matrix4f javaMatrix;
float[] openglMatrix = new float[] {
javaMatrix.m00, javaMatrix.m10, javaMatrix.m20, javaMatrix.m30,
javaMatrix.m01, javaMatrix.m11, javaMatrix.m21, javaMatrix.m31,
javaMatrix.m02, javaMatrix.m12, javaMatrix.m22, javaMatrix.m32,
javaMatrix.m03, javaMatrix.m13, javaMatrix.m23, javaMatrix.m33
};
To pass the matrix to OpenGL you should then call either
glLoadMatrixf(openglMatrix);
or
glMultMatrixf(openglMatrix);
depending on what you’re trying to do.
If you’re not familiar with OpenGL matrix stuff you might also want to check out the documentation on glMatrixMode, glPushMatrix and glPopMatrix.