After some years of use, exhaust manifolds get covered with soot, grease, and rust. One reason for this is that they are made up of cast iron and hence you need to take following precautions to clean them.
Step 1 - Remove the Manifold
To avoid any injury, let the engine cool off for around 30 minutes. Spray some solvent on the bolts which are on manifold heat shield and then remove them. Then remove bolts from the manifold. You would need to use a socket wrench to remove these bolts as they are tightly screwed and difficult to remove, even after applying a solvent. Now detach exhaust manifold from vehicle.
Step 2 - Clean and Re-install
Apply some lacquer thinner and use a scrub brush to vigorously scrub it. You would need to scrub the manifold again and again after letting it sit for a while till you are satisfied with the appearance. Once you are done, thoroughly wipe the manifold and apply some dressing. This is not necessary but it will protect the manifold from rust for a longer time. Now re-install your exhaust manifold, and the heat shield.