If you need to take your work on the road, there's no substitute for a decent laptop. Unfortunately, the light weight and versatility that make laptops so useful also make them fragile. If something vital breaks, like your screen, that can really ruin your afternoon. If your laptop has a broken screen, you can use an external monitor as a workaround, which at least lets you work constructively until you repair or replace the computer.
Look at Your Options
Your laptop should have at least one connection for an external monitor and could have more. The oldest and most common is the 15-pin VGA connector. It's still used pretty widely for computer monitors, and it's a common option for projectors and other accessories. You might also have an HDMI port, a DisplayPort – which looks like an HDMI connector with one side flattened – or a DVI connection. If you're buying or borrowing a monitor to use with your laptop until it's repaired, it's simplest to look for one that's got the same connector. If that's not an option, you'll have to buy an adapter, which is an added expense but not usually a major one.
Hopefully, you already have a suitable cable or will get one with the monitor – otherwise you'll need to pick it up from your local office supplier or tech retailer. Connecting is usually pretty straightforward. If you have a VGA cable, screw it into the thumbscrews on the back or side of the monitor, then connect the other end to your laptop. It'll fit only one way. Most laptops don't have thumbscrews to hold the connector in place, so once you push it in, you're done. With HDMI, DisplayPort or DVI cables, you'll do the same, though you won't need to tighten screws at the monitor end. There's enough friction in the connector to keep the cable in place during normal usage.
Switching to the External Monitor
Now turn on your monitor and start your computer. Most newer laptops are able to recognize when an external monitor is attached and will recognize it automatically. If that's the case, you'll see your regular boot-up and login screens scrolling past on the new monitor. If it's not recognized automatically, you'll need to use your laptop's function or Fn keys to switch manually to the external monitor. These vary by brand. For example, on an Acer Aspire One, the external monitor keystroke is to hold down the Fn key and tap the F5 function key at the top of the keyboard. On many HP models, the combination is Fn and F4. You'll usually see a little monitor-shaped icon on the correct key, or you can use another machine to search the manufacturer's website and find out the correct key for your laptop. Once you enter the keystroke and let go of the keys, your external monitor should come on.
If It Doesn't Work
If the laptop with the broken screen won't connect to the monitor, it's still not quite time to panic. First, try just tapping the keystroke again. Some laptops have three choices, internal, external and both, and you may need to tap it more than once to get the correct mode. You may also just have a faulty cable. Low-cost HDMI cables, in particular, are often rather "iffy." Try a different cable if you can. If that isn't an option, try the same cable on a different device, like a TV, to see if it works there. If not, you need a new cable. If it works fine on other devices, then it might be your computer's video card that's at fault, rather than the screen. If that's the case, you'll probably need to bite the bullet and start budgeting for either a repair or a new laptop.