We use On the one hand with positive ideas (On the one hand + postive ideas).
We use On the other hand with contrasting or opposing ideas (On the other hand + contrasting/ opposing) ideas).

 

   E.g 1: On the one hand, England is a beautiful and interesting country.
              On the other hand, the weather is not good.
             
   E.g 2: On the one hand, I can enjoy the beautiful fresh morning air.
              On the other hand, it is in the middle of winter and it’s a little bit cold.
             
   E.g 3: On the one hand, working from home saves time, as it is not necessary to travel to work.

              On the other hand, I could become very lonely.

   E.g 4: On the one hand, that movie had fantastic special effects.
              On the other hand, it was a little bit too long.
             
   E.g 5: On the one hand, travelling abroad broadens the mind.
              On the other hand, it can be expensive for some.

 

However, we should avoid these mistakes:
1. Don't write sentences that don’t give the contrasting ideas:
      E.g: On the one hand, travelling abroad enables us to have new experiences.
              On the other hand, it allows us to gain an understanding of other cultures.
             

It would be better if we write:
      E.g: On the one hand, travelling abroad broadens the mind.
              On the other hand, it can be expensive for some.
       
2. It follows with a list:
      E.g: On the one hand, there are many advantages to travelling abroad … + advantages 1, 2, 3 etc
              On the other hand, there are also many disadvantages … + disadvantages 1, 2, 3 etc