Part of being in a relationship is about dealing with tough times and getting passed hardships. One issue you might face with your boyfriend is the death of his father, which can be a challenging time for both of you. Consoling your boyfriend through the grave loss of his father will demonstrate your love and support and can help ease him through his grieving process.
Talk to him and make it clear that you are available during this trying time. Simply knowing you are there and that the lines of communication are open can be consoling.
Offer specific ways to help rather than saying, "I'm here for you." Prepare meals for him in advance; do his laundry; clean the house; walk the dog. Helping him get through the day reminds him that he isn't in this alone.
Listen when he is ready to talk. Allow him to air his feelings without talking about how you feel. Avoid trying to empathize by talking about tough situations you've been through. Although you mean to help, it can seem like you are saying that his grief is no different than anyone else's. Don't give unsolicited advice, which can be irritating to a person who needs to grieve and talk about his emotions.
Be there for him physically as well as emotionally. This doesn't mean that you have to be intimate in a sexual way. Genuine affection in the form of a comforting arm around his shoulders, hugs, or cuddling in bed can demonstrate your care and concern.
Watch that his grieving does not become detrimental to him. It is perfectly acceptable for him to want to avoid doing things or even avoid talking to people during this time. But turning to substances, or threatening harm on himself are signals that he may need professional help. If you notice these signs, talk to his loved ones about options, or offer suggestions for support groups or grief counselors in the area.