What are the two general ways through which an animal virus enters a cell?

One way is through endocytosis by tricking the host cell into thinking that the virus is valuable and then the virus ends up endocytosing it. The viral particle becomes enveloped by the membrane of the host cell until the membrane pinches off around the viral particle which results in the virus being inside of the host cell.

The other way is via fusion which is only done by viruses that have an envelope. The virus binds to a receptor on the host cell and then the membrane of the host cell joins together with the envelope of the virus that is infecting it (fused together). So, the animal virus can gain entry into the hosts cell through endocytosis or fusion between the host cell membrane and the viral envelope. 

hope this helps :)