It totally depends on what type of cough you have or if you are suffering from a cold or fever also with the cough. Sometimes you may have a fever with the cough and then you will have to treat it as per the condition. So, I believe this question is a bit vague to answer, but I can surely give you some tips to treat cough using some home remedies or at least to soothe your itchy throat.

Firstly, try to understand that coughing is a way for your body to expel phlegm, but sometimes one has a dry cough also which is a bit frustrating, and to treat them it is always better to seek a doctor's advice as they will be able to diagnose you better physically. Having said that, there are some steps that you can take to keep your itchy throat in check;

1. Do salt gargles:
   Doing warm salt gargles can be helpful if you have a sore throat or if your throat is feeling itchy day in and day out. You should take half a spoon of salt and mix it in a glass of warm water (which will be around 240 ml). 
   
   Many people do gargles at night only. But it is better to do gargles after a few hours itself, so as a rule of thumb, you should do gargles at least 3 times a day. This will help you in soothing your throat much faster.
    
2. Take steam:
   Nowadays there are several medical steamers available in drug stores. You can use them or just can boil water in a bowl and add some peppermint or steam tablets to your boiling water.
   
   Ensure that you have switched off any air conditioner or fan and keep a towel on your head while you take steam. But be careful because steam is more hot than boiling water, so it is better to keep some distance while taking steam.
   
   You can even think of taking a hot water bath, which will have a soothing effect on your throat, especially if you don't have a fever. 
    
3. Drink a lot of water:
   Usually, when we have a cough, we tend to drink less water because of the irritation or itchy feeling in our throat, but this is the time when you should drink more water. Staying hydrated is essential to good health and maybe even more important when you are recovering. 
   
   If it is getting difficult to drink water, then keep a bottle filled with warm water and sip water every half an hour or so. You can also try alternatives like tea, soups, etc.
    
4. Drink ginger tea:
   Ginger helps in boosting immunity, so drinking ginger tea is a great way to recover from a cough. We even have an advantage in Kashmiri culture of having Kehva, which can be used to soothe your throat by mixing a bit of honey and ginger in it and having it when you feel itchy in your throat. This is also a great way to keep yourself hydrated.
    
5. Take rest:
   Even if you are working from home, take a leave from your work. This is important because your body needs time to recover, and this can only happen if you take a good nap. Your body recovers faster when you take a rest. And by rest, I don't mean you scrolling social media websites, but to take a good nap.
    
6. Eat nutritious food:
   While recovering it is always better to eat a healthy diet and say no to junk food. Instead choose fruits, vegetables, whole grains, low-fat dairy, and lean protein for nourishment. You can even have a chicken soup that will help you in gaining strength while recovering.
    
7. Quit smoking or be away from dusty places:
   Smoking or being at dusty places can make your cough worse. This is because our body is already trying to get rid of things that have made us sick, and if you smoke or are in a dusty place, the particles can stick to your throat and make you feel itchier. Even if you have to go out, use a mask to save yourself from dust and others from your cough. 
8. Take over-the-counter cough candies:
   There are several candies, for example, peppermint candies, etc that help in soothing the throat, you can use them when you feel you have more itching in your throat. 
    
9. See a doctor if your cough gets worse:
   In many situations, a dry cough will go away within a week or two. But in case you don't see any improvement, and you may see a lot more phlegm coming out, or you feel weird sounds while inhaling or exhaling breath, then you should definitely go a see a doctor.
    
10. Never take any medicine without a doctor's prescription:
    It is important to understand that when weather changes happen, we see a rise in cough and cold, but we should always try and consult a medical practitioner before taking any medicines, because that may have an effect on our immunity as a whole. You can treat symptoms like fever using over-the-counter tablets, but it is always better to seek medical advice before treating yourself.

Conclusion;
Although cough can be treated at home, it is always better to seek a medical practitioner's advice because they only can diagnose the reason behind your cough. Even before treating your cough yourself, go and seek advice from a doctor. Having said that this article is just to help you treat your cough at home, and it should not be taken as medical advice, as it is vague and doesn't take into account all other details or medical history.

Have a speedy recovery :)