There will almost certainly be things I miss so don't hesitate to comment corrections or suggestions. Also this was all tested in Starlights mapping server. There are probably differences with Issy's but I havent found them yet. I will comment below if/when I do.

Now the basics

Your Tools

Forensic Scanner

The bread and butter of investigations. Scanning practically anything will show three things. The fingerprints of anyone that touched it (if they wore no gloves), the fibers of any gloved hands that touched it, and or the residue of anything used to clean it. I have included a list of fibers and residues, and their causes based on Lithenheads video and my own experiments in a mapping server.
(I could swear damp rags could be used to remove evidence and that they left grey fibers in the residue section but I could not seem to make that happen in mapping. If anyone knows what going on there please let me know!)

Log Probe

Your PDA comes with a logprobe, There is also a cartridge in your locker, This is a very underutilized tool. It can be used on Airlocks, air alarms, vendors, lockers, and basically anything that needs access. It will display what ID, Borg, or AI used it, along with the time. There are exceptions. On airlocks if the log wire is cut, future logs will not be recorded until that is fixed. You can check this by opening the door yourself, and rescanning. Also, if a multitool is used on a log wire, the logs will display an "Error: Electromagnetic Spike" message, along with the time. This can be handy for showing when a door was hacked. If the ID has no name, it will display only the job in brackets. for example the spare captian ID shows up as "Time: (Captain)". If there is no name or job title attached to and ID it will only show as brackets. Holding an ID in hand removes the name of the ID, but does leave the job. Interestingly, (at least to me) Access breakers seem to remove previous logs from lockers, but not doors.

Forensic pads. Forensic pads can be used to collect fingerprints from suspects. Just left click on an ungloved person with it. You will need to examain the pad after to see the prints. Fun fact you can then tap it on your scanner and it will make a noise and display a message to show if the prints on the pad match any on what the scanner last scanned.

Security Records console There should be one in your office. It contains various information about all the crew on the manifest. This includes theier species, name, job, and DNA and fingerprints. This is how you can actually use the forensics you have gathered. The records deleting event (I forget the name sorry!) Can remove people and their information from the manifest so be aware of that.

General (and unorganised) Tips and tricks:

Weapons can have the DNA of who they were used on. Since antags hide their weapons (or at least they should) this is most useful if the victim managed to hit back in self defence, Make sure to check the knuckleduster of any dead QMs! But don't be afraid to scan any weapons you find in the bags of suspects. Dont just lock them in the contraband crate.
Faxed Sydicate Business cards dont carry prints with them but normal paper does.
Half eaten foods and glasses have dna of those that ate/drank from them
Logprobes have a secondary use. Hunting fleeing suspects. Just follow the route and you will eventually find them.
If the attacker has been damaged enough to leave blood and not cleaned up after themselves you can scan the puddle for DNA. But even a glance at the colour can give you vital info. For example the majority of species have red blood but other species have colours like blue vox blood or slime for slimes.
Checking the shift time when you first hear of a crime and getting an estimate for how long before that it happened can help narrow down what logs to pay attention to.
Even antags that are prepared enough to cut door logs usually only start doing that when they get to where they plan to crime. trace back where they likely came from and check the surrounding airlocks.
Lockers and backpacks aren't the only place contra can be hidden. Be sure to check for unpowered disposal units and in potted plants and toilets.

The main skills that will help you the most in your detective journey is patience and determination. All crimes can be solved if you spend enough time on it. That being said, you dont always have that time, nor should you. As with all things in SS14, its not about winning. A game of cat and mouse isn't fun if the cat always wins. So make sure you and that slippery thief youre chasing have fun. (Also consider making our poor, stressed ward players happy with a folder of all your evidence and notes). Now grab a pack of ciggys (Nomads only) and your revolver you definitely wont slip with and lose in maints and go catch your next bad guy!