Lets say you want to search a room for clues. The GM might tell you to roll a Perception + Intuition [mental] (3) test. Your perception (skill) is 3, so you pick up three dice. Your intuition (stat) is 5, so you add five more dice, for a total of 8. It's a little dark in the room, so the GM gives you a -1 penalty for lighting, so you subtract one dice, leaving 7. You roll them, and get 1, 1, 4, 5, 5, 6, 6. Four of your dice show 5's or 6's, so you have 4 Hits. You now compare this to your mental limit, which is 3. Since you have more hits than your limit, you lose the excess and keep 3 hits. Your final hits (3) are equal to or greater than the Threshold (3) you succed! The GM tells you what you found.
Extended tests: let's say you're trying to fix a broken commlink. The GM says it's a Hardware + Logic [mental] (10, 1 hour) extended test. You have hardware 4, logic 4, so you roll 8 dice. Your first roll is very high, getting you 6 hits, but your mental limit is 5, so you only get five of them. In the first hour, you've managed to get about half the work done. You're still free for a couple hours, so you roll again, this time getting only one hit, for a total of 6. You keep going for a third hour, rolling again and getting another 3 hits, for a total of 9, one short of the threshold. Sadly, your team has a meet with a contact in 30 minutes, so you don't have time to make another roll now. When you get back, you can spend another hour and likely get the one hit you need to finish fixing it.
Versus tests: the drek has hit the fan and you're in a shootout with a security guard. You draw your pistol and take a shot. It's a Pistols + Agility [accuracy] vs. Reaction + Intuition test. Note that in this case your limit is the accurcay rating of the weapon, rather than your physical limit. Also note that the defender is rolling Stat + Stat in this instance, as there is no specific skill for dodging bullets. You have Pistols 5 + Agility 6, +2 dice for a smartlink (13 dice), with a limit of 6 for your pistol. You roll and get 4 hits: since this is lower than your limit, you keep them all. The defender rolls his reaction 4 + intuition 3 (7 dice) and gets two hits (note that there is no limit applied to the defender: this is always the case in versus tests, as far as I am aware). Since you have two hits more than him, you successfully shoot him, dealing damage based on the gun.
There are a couple more rules to learn (like Glitches), but this rundown will hopefully help you understand the rules well enough to read through them on your own without needing assistance. Still, if you have any further questions, don't hesitate to ask, there are plenty of people here willing to help.