Checking what Virtual Local Area Network you're on may not be possible, depending on the network hardware you're using and its drivers. Packets are tagged with the VLAN they belong to, however the operating system will often strip away the VLAN tag. Even if you're capturing packets, you may not be able to find your VLAN ID. If you can access the switch you're connected to, then it's a matter of logging in and checking the settings. If you don't have any VLANs configured, then you're on VLAN 1, by default.
Connect to your VLAN using your Ethernet cable.
Open your packet analyzer program. Select the network card to listen to; you'll want to select the one connected to your VLAN.
Scan the incoming packets to your computer; these are the ones that are going to be labeled. Look for the VLAN ID, which will be listed under an "802.1Q" heading.