Low sec space is 0.4 and down to 0.1. In low sec people may attack you and they will only suffer a small security rating loss and the station and gate guns will fire at them. Otherwise there are no penalties. Obviously pirates roam this region looking for easy kills.
When in low sec or null sec your local chat window is an essential tool. You should have it somewhere you can see it all the time. My local chat is separate from all other chat windows allowing me to always see in a glance who is in the system. You should always know when someone has entered the system. No AFK moments in low sec unless you cloak somewhere safe. If you see someone enter your system you should immediately decide how to deal with it. Leaving the system or docking is the safest option. Going to a safespot (see below) and cloaking is next best. Lastly hanging in a safespot is mostly safe as long as you watch for probes. If you choose to continue what you are doing, then you should be prepared for company. Move away from standard warp in points. Keep an eye on your overview for ships. Use your directional scanner (see below).
Safespots are places you cannot warp to using the system menu. That means they are away from normal features like planets, moons and belts. You can only be found in a safespot by combat scanner probes or if you have shared your safespot. To make a safespot first open the map and go to the solar system view. Find two places you can warp to like planets or gates that are far apart. Warp to one. Now open the People and Places window and go to Places tab. Warp to your other target. While in warp, before reaching the other end, click the "Add location" button and save a bookmark. Don't name it yet, you need to be fast. The bookmark should show as an icon in the map view. It should have marked a spot part way between the two planets/gates/etc that you were warping between. This is often enough but for more security you can go one step further. Warp to the bookmark you made. Now warp to a different celestial object and bookmark another spot. This spot should be completely off the paths between planets/gates/stations/etc. You should rename your bookmark and put it in a SAFESPOT folder. Its worth making safespots as the first thing you do in a system. You may even need them in high sec if a war breaks out.
The Directional Scanner
The Scanner is the button middle left of the HUD. It has three modes. You need the tab called Directional Scanner. You can use the DS as a early warning system and intel gathering tool. The max range on the Scanner is about 14.5 AU but you can set that in the range box. Check the "Use overview settings" box to give a scan of all ships in range. Uncheck it to see if someone has combat scanner probes (or Sisters combat scanner probes) out looking for you. Use the scanner to determine what the newest person in local is flying and is he likely to be a threat. You can detect people coming towards you by setting the scanner to 1-2 AU and scanning regularly. If someone shows up then they are close.
Consider adding probes to your overview setting to make scanning for them easier.
The directional scanner can be used to find people in a system but that is an advanced technique. Be aware that if you can see them on the scanner they can see you and maybe find you. Cloaked ships don't show up on the scanner.
Its a Killing Field Out There
Don't assume that people need a reason to shoot you. They have one. You are worth points on their killboard. People will kill you for no other reason. Some people will act friendly afterward but they are after ship kills and will probably kill you again if they get the chance. They will also kill your pod. Sometimes you can pay a ransom to escape death but pirates aren't known for their trustworthiness.
The Price of Survival is Eternal Vigilance
In low sec you must always be alert to danger. You cannot afford to go AFK without a cloak. You should always be watching local and always know when someone enters the system. If you must go afk either cloak in a safespot or leave. Another thing you need to do is plan your escape in advance. Many pilots lose their chance to escape trying to decide what to do. Try to avoid dying to indecision or panic. Its worth aligning to a celestial object so you can warp almost instantly. Also you should avoid being at the most likely warp in point for a aggressor. That means don't be at 0 km on a belt or right next to the warp in point for a complex. Remember that an overloaded tech 2 Warp Disruptor can manage about 28.8km You should be much further away than this.
Getting Caught on a Gate
The most dangerous places in Low Sec or Null Sec are gates and stations. This is where people will wait for you. If you go through a gate and find enemy on the other side remember that you have 30 seconds of gate cloak. Take a little time to assess the situation and let your client load everything. This will avoid the system lagging when you move. You should also let the session timer run out. This is only about 10 seconds now so its done quickly. If there were no enemy on the previous side of the gate then your best option is to run back to the gate and jump through. If the enemy attack you they wont be able to use the gate. Remember to not attack. If you attack someone, the gate will refuse you access for 30 seconds.
Null sec is 0.0 space. Its important to note that things get more dangerous as you go from one to the other. You must always know what sort of space you are in or going to. The first system of 0.0 in a pipe is usually camped and often has a warp disruption bubble established at the gate. This is an area effect warp disruptor so you will be unable to warp inside the bubble.
There are no rules in most 0.0 space. People may attack you with no consequences there. In addition devices like warp bubbles and Bombs are allowed to work in 0.0 space. These make gates and stations very dangerous as you could be trapped away from safety.
Its important to remember that in Non-NPC space (eg Serpentis) the stations are owned by alliances. That means they decide who is allowed to dock. Usually that means you cannot dock in alliance space.
Warp bubbles are area effect warp disruptors. You cannot go to warp inside these bubbles (with one exception). They can be haulled and anchored like cans or they can be fitted to Interdictors and Heavy Interdictors. They will pull you out of warp short of your target or suck you beyond your target if they are in line with your warp. This means you will be a long way from safety and probably surrounded. In 0.0 space it is never a good idea to warp between one gate/station and another directly. People set up bubbles to catch those that do. You are better off warping to a celestial off to one side and coming in at an angle. The best solution though is to have tactical warp points set up (see below).
If you come through a gate and discover you are in a bubble and there are ships waiting for you then the best way to escape is to do the following. Wait for your session timer to run out then run back to the gate at full speed and jump through. Hopefully no-one will stop you and you can escape on the other side.
These are bookmarks at stations, POS and Gates that are over 150km away from the feature but are close enough to see if a bubble or camp is there. 250-300km is ideal. You will be able to warp from a tactical to the gate/station/etc if its clear and avoid traps. To make them you just need a fast ship. Keep your tactical bookmarks in a separate folder for easy reference. They will always be useful.