The medical term for a lung clot is a pulmonary embolism, often shortened to a "PE" by doctors. A clot in the lungs can lead to a wide scope of symptoms.
The typical symptoms are: Pleuritic pain (pain made worse by a deep breath), shortness of breath at rest or on exertion and possibly haemoptysis (coughing up blood). The symptoms will usually have a sudden onset, sometimes proceeded by a pain or swelling in one of your calves (more on this later!). If a clot is severe, it can cause damage to the right side of your heart. If it is very severe, it can cause a sudden collapse or even in extreme circumstances, sudden death. 

The picture we're trying to paint here is that depending on the size and location of your clot, there is a wide spectrum of possible outcomes. Before reading on - we'd highly suggest you read about the lung vessels in our general overview. 

To give those of you too lazy to read the general overview (I count myself amongst you), let's follow the journey of a common clot to give you a sense of the anatomy.

On a long, fourteen hour flight, a person doesn't move much. Without walking, the calf muscles aren't contracting and the blood within the deep vein running through them hangs about like a bad smell. When blood is static for too long in one area, it's more likely to clot. So, a clot forms in the deep vein of the leg - this is called a DVT (Deep Vein Thrombosis). This will cause calf pain or swelling in one of your legs.

The eager traveller ignores the pain, ascribing it to a muscular cramp and moves on. As they walk to the baggage claim, the calf muscles squeeze the clot - a part of the clot dislodges. The clot travels up the vein, past the groin, through the abdomen and returns to the right atrium of the heart. Then it is moved into the right ventricle before being propelled towards the lungs via the pulmonary trunk.

If the clot is really big, it'll get stuck here, at the point that the trunk divides into the left and right pulmonary arteries. This is called a saddle embolism. This is the most dangerous type of PE. However, oftentimes the clot isn't totally occlusive, meaning that some blood can still move around the clot into the lung - and that's good news!

If the clot is smaller, it will travel into the right or left lung via the pulmonary artery. This main artery then branches into smaller and smaller arteries spreading out across the lung. Eventually, the vessel will become so narrow that the clot gets stuck - causing a PE. 

If the doctors suspect a PE, they may order a d-dimer. It's a controversial blood test. Basically, if it's negative, you don't have a clot. If it's positive, you may or may not have a clot. So it's only really useful if it comes back negative. Some doctors might skip this all together if your story really adds up to a clot. 

The confirmatory test is a CT scan with contrast called a CTPA (Computed Tomography Pulmonary Angiogram) - nevermind the jargon, basically it lights your lung vessels up like a Christmas tree - looking for any blockages in the white river. It can identify the clot, or clots - determine if they are causing any obstruction to blood flow, and also if there is any area of damaged lung from a lack of blood supply (lung infarct). 

The lung infarct is usually what's causing your pain. It hurts when you take a deep breath because the first place to start taking damage from the lack of blood supply is the lung on the edges (furthest from the big vessels) - when you take a deep breath, you press this region up against the ribcage and sensitive, inflamed pleura (outer membrane). 
The lung infarct can also bleed into the airway, causing you to cough blood. 
The cool thing about the lung is that it has another arterial supply - the bronchial artery. It can take quite a beating from an occlusive lung clot and still fully recover once it's treated. 

Once a clot is confirmed, we start blood thinning treatment (anti-coagulation). Usually, we will start with injections of clexane in the tummy, and a few days into your admission we will start a tablet form of a blood thinner (usually apixaban or rivaroxaban). 
If your clot is provoked (you had a recent surgery and spent the last three weeks on the couch eating cake) - we will treat you for three months. 
If your clot is unprovoked (we have no idea why it happened) - we will treat you for six months.
If you get a second clot, or have a high risk of clotting (genetics, etc.) - you may need lifelong therapy with blood thinners (known as anticoagulation). 

If we don't know what caused your clot, we will send a blood test called a thrombophilia screen to see if you have a genetic predisposition. 

Unfortunately, if you have a sudden clot out of nowhere with no clear cause - the doctors will have to investigate for a hidden, influencing factor - namely cancer. Malignancy increases the likelihood of clotting as it is a pro-inflammatory state. Your doctor may ask you general screening questions - Have you lost any weight recently? Any night sweats? etc. 
We may also consider scanning your abdomen and pelvis to search for any masses. 

In this instance, we are just being cautious. It is perfectly possible to have a clot for no clear reason - sometimes you're just unlucky!

The last thing we'll talk about is the right side of your heart. If there's a blockage in the pulmonary artery, the right ventricle has to work extra hard to pump blood around it. This can cause strain on the heart and lead to symptoms of right-sided heart failure. 
When you come into the ED, we will do a few basic tests such as a blood test looking for a raised troponin (heart marker) or any changes on your ECG to suggest right-heart strain. Your consultant may also ask for an echocardiogram (ultrasound) to look for any structural abnormalities. Once the clot is gone, the heart usually makes a full recovery - so we'll repeat the echo in about 4 - 6 months to make sure!