Yes, you can get WIFI with satellite internet. In fact, Viasat satellite internet gives you everything you need to get a wireless network started when you first sign up for a plan. When getting a service package with Viasat a technician comes to your house and installs the satellite dish and gives the modem and wireless router with an ethernet cable to the customer. If you already have a router that you like using then it doesn't have to be replaced.
When adding WIFI it is necessary to choose a router, either one the customer chooses or one your provider provides. The router should then be plugged into a wall outlet and powered on. The router needs to be connected to the modem and the customer needs to configure the network. At this point the wireless network will be working and can be used this way, but most people change the network name and password to make it easier to remember since the default network and password are generic. To change the password there should be a sticker on the router with steps to change the settings. It will most likely be the IP address you put into the web browser and once on the website, input the default username and password on the router. On the next page you should be able to change the password, network name and the network security to WPA, which is the most secure type of network. This should be all you need to do, so you can select the network on your phone or computer, use your new password to log in and you should be on the new WIFI you set up.