What do Hrothgar and his council do to try to save his guest-hall?
I think that the answer you are probably looking for is that they performed sacrifices to the gods to try to save the guest hall.
You can find this in Chapter 2 of the poem, right at the end. Grendel has been killing Hrothgar's thanes and they have not been able to figure out any way to stop him. So what they did was to sacrifice at "heathen shrines" to ask the "slayer of souls" to help them.
Since the poem was written down in Christian times, the poet criticizes this practice, saying that it was hellish and that they would have done much better if they had been Christian and known the true God.
Hrothgar and the Danes do very little to try to save their mead hall, Herot (spellings vary with translations). After Unferth taunted Beowulf's abilities as a warrior, Beowulf says that one of the reasons he has come to fight their monster, Grendel, is because the Danes aren't fighting him themselves. He says that the monster has learned that he can come for the Danish people with no fear of reprisal. Grendel doesn't find fighting when he comes to Herot, he finds food and delight as he murders, gorges, and feasts on the flesh of the Danes.
In the epic poem "Beowulf" Hrothgar and his men are plagued by the murderous monster Grendal. Hrothgar's kingdom is besieged by the monster that sneaks in and kills the people for a period of twelve years. The hall had remained empty, but Hrothgar and the council deside that thye should move into it because it is a safe place where they would all be together (safety in numbers) and Grendal would never step into his throne area.
Hrothgar and his council went to Beowulf with offerings of money and payment in hopes that he would stop murdering Hrothgar's people. This continued to fail. Since the monster is from hell itself they act pagan and set up alters and make offering sin hopes of stopping Grendal's wrath. After Beowulf shows up they implore him to help them for a reward.