Yes you have to be careful and ask questions, and check specifications carefully. I only buy from private sellers. You can usually tell by the listing how up front they are. The good sellers will give a lot of detail and say how long the battery lasts, whether the battery and charger are original and so on.
Here's my checklist for what's in the listing, or if not, what to ask.
1) How long does the battery last and is it the original/genuine one.
2) Does it come with a charger and is it the original one
(Good sellers should say both those things in the listings)
3) Does it still have the original recovery partition?
(eg if it is Windows 7 or 8 someone may have reinstalled and wiped out the original recovery partition - you need the original recovery partition to ensure the original manufacturer software can be reinstalled. If there is no recovery partition, you can install the Windows software yourself providing you have the licence key on the bottom - Microsoft allow you to make a disc with the Windows software on and then you just type in the licence key). If it's been upgraded to Windows 10 and is running Windows 10 you need to know that the Windows 7 licence product key is still readable on the base - in case you ever need to reinstall Windows 7 mainly.
4) What is the processor? This information should be in the listing. To get the kind of laptop you want that will be good you need to know - what the processor is (ie is it Intel i3, Intel i5, Intel Pentium). Part of the reason we get them second hand is because you can get a higher specification, faster laptop, than you can afford new. Intel i3 and Intel i5 are both good. You need i5 if you want to do video editing.
5) What is the graphics? Most laptops will have Intel integrated graphics, which is fine. But if you want to do video editing you need either Intel HD graphics or other dedicated graphics like Nvidia or AMD Radeon. As Nvidia or AMD Radeon laptops tend to cost more, I go midway with Intel HD graphics which are enough for basic video editing if you have an i3 or i5 processor. If you're not bothered about video editing then an Intel i3 laptop is quite quick and any graphics will do fine.
6) What size hard drive does it have? A hard drive can be replaced for about £30 with a brand new 500GB one, so that isn't such an issue. Some sellers will have wiped the hard drive and reinstalled the software to factory settings. To protect themselves from their old data being on the disc. Most sellers don't and just restore to factory settings via the recovery data on the laptop. That is more their problem than yours, providing you keep the details of the date of sale/purchase to show the date you owned it from.
7) Does it have any damage or parts broken or missing? The listing should say if there is any damage or any scratches to the screen or if it is in good cosmetic condition with only minor scratches and no damage to the screen. If it doesn't say give much information on condition, then be suspicious. Avoid anything that has a dent on top or any kind of damage as it's likely to have been dropped, even if the seller says it's working fine.
How much RAM is installed (you want a minimum of 2GB. 4GB or 8GB is ideal).
I only get ones that have genuine batteries and chargers, not replacement ones as replacement non original batteries or chargers can be a fire risk.
Postage: Whatever postage they quote I always ask for Parcelforce 48 which has Insurance during transit and is tracked. It costs about £19, so if the postage is quoted as £10 for second class, I offer to pay the additional £9 and ask for it to be sent by Parcelforce 48.
I only go for things from sellers who seem to be ordinary people - private sellers, with 100% feedback, and you can get a gut feeling from their description whether they sound genuine or not.
Anything that has a brief listing, without actual photos (eg stock photos) and very little information, is to be avoided really.
Bit long winded there, but that's my checklist. If you are prepared to accept something with a non functioning usb port for example, you can get a good bargain, for under £100 maybe, providing the other two usb's work ok. The one I just got cost £175 but is like a brand new laptop and hardly used with 3 hours battery life. It will run either Windows 7 or Windows 10 (it had the free upgrade to Windows 10 but I can still install Windows 7 from the original licence key). And comes with a nice laptop bag as well. It's fast, with an Intel i5 Processor and dedicated HD graphics.
One final check - if it has been upgraded to Windows 10, check out the model number on google to see if it is one that is suitable for upgrading and Windows 10 works well on it.
First thing to do after buying is turn it on and make recovery discs - in case you ever need to reinstall if the drive fails.
When searching it helps if you have an idea which one you want. eg Sony Vaio 14" (there are some good older models of those for about £80 but they will only run Windows 7 and not 10 usually and tend to be fine for general internet use but a bit slow for anything major). Or HP Pavilion DM4 (I got that one because we had one before and I like 14" laptops).
I only ever look for Sony Vaio's or Hp Pavilion DM4 because they're the devil I know. There are quite a lot of good used Sony Vaio's. They are very nice laptops. Sony don't make laptops any more, but they still have the software and drivers available on their website if you ever had a problem.
Apple Macs always go for a lot - not always much cheaper than a new one.