There are two cables or leads coming from your welding machine. One is the "work " lead and is used to supply power to the electrode. The other is the "ground" lead. You have to attach the ground lead to the metal your welding on, in some fashion, in order to complete the electrical circuit. If you don't have the ground connected, you can't strike an arc, because the circuit isn't completed. If your ground is connected, but for any reason is not making good contact with the metal, then the welding arc will be detrimentally affected because the circuit is not totally completed. Think about it like a kink in a garden hose, you still get water, but not as much as an un-kinked hose. Additionally if you have an uncompleted circuit, the "left over" current is looking for some place to go. If you were to grab the metal with bare sweaty skin with one hand, and then grab the bare end of the ground lead with the other hand, while your friend was welding on the metal, then your body would become part of the ground, and get shocked. If you had a well connected ground to start with, you probably wouldn't get shocked at all, or only very little.
By well connected, we mean that your ground cable should either have cam-lock twist connectors on the ends or securely fastened cable lugs with a bolthole. Make sure the connection at the machine is good and tight, with clean metal-to-metal contact. On the other end, either bolt the cable lug to your work, or attach a spring activated ground clamp. If you use a spring clamp, make sure it is firmly attached to the ground lead and is firmly clamped to the metal. If there is a bad connection on the ground lead somewhere, while welding, it will develop resistance and heat up. That means that if your ground clamp is too hot to touch, or the insulation is melting off the lead, you've got a bad connection and need to fix it.
Try this, run a piece of metal down your wood table leg from the floor to the metal tabletop. Weld the connection at the tabletop and weld a 1/2" bolt to the metal at the bottom of the table leg. Now you have a place to securely bolt your ground lead, effectively grounding your worktable, in a manner that allows the ground lead to lie flat on the floor, thus reducing a tripping hazard. Now if the metal you’re welding is touching the table top, it's grounded, and you can weld on it. Sometimes you'll want to apply a separate ground for better contact, and/or to keep your work from getting marked up where it grounds to the table, so attach a separate, short ground lead to the table top with a bolted connection, and a spring clamp on the other end to attach to the work. Now you're doubly grounded.
Does that answer your questions?
Good luck!
Tim