The lymphatic vessels are similar to veins, as the contain valves which ensure the one-way movement of the lymph. They do however, have much thinner walls than veins. In the lymphatic system, the lymph drains into venous blood through the right duct and the thoracic duct at the junction of the internal jugular and the subclavian veins.
The actual sequence of fluid flow is goes something like this: blood capillaries (blood) to interstitial spaces (interstitial fluid) to the lymphatic capillaries (lymph) which lead to the lymphatic vessels, to the lymph nodes (lymph) back to lymphatic vessels (lymph), then to lymphatic ducts (lymph), to the junction of the internal jugular and subclavian veins (blood). As mentioned before, the lymphatic system and the cardiovascular system work closely together.
There is also the matter of how the lymph is moved along this system. As a lymphatic vessel distends, the smooth muscle in its wall contracts, and this helps in moving the lymph from one segment of the vessel to the next segment. There is also the same two pumps that aid the return of venous blood to the heart that maintains the flow of lymph, and these are the skeletal muscle pump and the respiratory pump. So the one way flow of lymph is caused by skeletal muscle contractions and respiratory movements.
The skeletal muscle pump works in the milking action of the skeletal muscle contractions compresses the lymphatic vessels and veins. this forces lymph toward the junction of the internal jugular and the subclavian. The Respiratory pump works by having the lymph flow maintained by pressure changes that occur during respiration. When you breath in (inspire) lymph flows from the abdominal region where the pressure is higher, toward the thoracic region, where the pressure is lower. When you breath out, however, the valves help to prevent back flow of lymph keeping it a one way pump.
So its pretty cool to see how the two systems work so closely together to maintain a balance in fluids in our bodies. Although extremely different from veins, lymphatic vessels carry out fluid to the different regions of the body like the cardiovascular system carries blood to the different regions of the body. This way we are able to ward off infections that happen in our extremities or abdomen.