How I can be more empathetic and caring towards my long distance girlfriend?

Hello.  It is great that you are making the effort to learn how to be more empathetic. That is a great first step!  There are many ways to show empathy.  One way is to truly listen to what your girlfriend is saying. Allow her to express herself without judgement.  Often depression makes it difficult for others to feel like they are being heard. Sometimes people feel judged easily. Try to think about how you would feel when experiencing similar things and respond accordingly.  Reflective listening is a technique to help show empathy. This involves listening to what a person says and essentially repeating it back to them so they see that you hear them.  This helps to acknowledge what the person is feeling, which is very important. We never want to make someone feel like their feelings are invalid. Be mindful not to give unsolicited advice. Listening is more helpful. Body language is important as well.  Try to have good eye contact and be present.  Keep distractions at minimum while interacting with your girlfriend. 

We often want to relieve our loved ones of pain and help in any way.  It's important to allow your girlfriend to feel like she can express her needs to you.  Sometimes it is possible to intuit the needs of others so you may be able to identify things that will make her life less stressful.  Sometimes that may be simple things like helping with chores, making dinner, or picking up things from the grocery store.   Be mindful that it may not be in your power to reduce her stress, depending on the source.  Sometimes, the mere act of offering help is helpful.

Another suggestion is to educate yourself on depression.  Even though depression can look differently from person to person,  learning about the facts and symptoms of depression can help you be more empathetic with your girlfriend.   Be patient with her as well.  It may not seem like her depression is improving. It often takes time and trial and error before improvements are noticeable.  Depression may never truly go away.  It may be a life long presence in her life, but it definitely possible that she learns to cope and move forward.  I hope this helps!