Always be suspicious. I know people all too ready to read emails fom their bank. Ask yourself did you ever give your bank your email address? Not just banks but no reputable organisation will ever ask you to give out information like a PIN. I will also digress and argue we need to make as much care with phone calls. Sometimes my bank rings me and I won't cooperate. They want me to confirm certain personal details but I say I don't know who you are. The same logic should be applied to the Internet. I know people who end up, at worst with tons of spam, because they respond to unsolicited emails offering them, say, a free iPad. Unfortunately peoples greed trumps common sense. Seriously, who is going to send out an email offering you for free an expensive device. How did they get your email? How did they even know you exist?
As most people do not have enough savvy to avoid problems they should have in place at the very least a firewall and an anti-malware program. Do not be fooled in to paying for expensive ones. There are many excellent free ones out there. Do not relyon Microsofts. They never as good as alternatives.
Be careful when downloading software. Nowadays even software that is designed to protect your computer will offer you crapware. Never just click OK, Next, Continue buttons. Read every screen and make sure you are not agreeing to download something that at best you do not need and at worst may damage your computer.
No one goes on holiday for a fortnight and leaves all their extenal doors and windows unlocked and open. Apply as much security to any method of entry to your computer as you would your home. The Internet is a wonderful place but there are people out there who will use it for their own nefarious ends.