The Investigation skill has a fair few obvious uses so this one is often not so tricky to put into into the game or remember to use. The best rule of thumb for it is whether a private investigator or police officer would be handy in this kind of situation. If they would be, odds are there's some sort of investigating to do. Be aware, though, that some Storytellers won't allow you to "Roll X to complete the plot" so while you'll get a bunch of clues, hints, and possibly some suggested leads, don't be surprised if it stops well short of solving everything.
Often you can also get more traction with your Storyteller if you suggest possible things to investigate rather than "Rolling X to investigate the house". If you're in a murdered house you could mention that you're looking for tire tracks in the dirt driveway, entrance and exit points (jemmied windows, broken glass), or for mail, diaries, and medicine (medicine can give strong clues as to the state of the owner's mind). It's worthwhile doing this as it lets the Storyteller know you're putting in extra effort (and they often like to reward effort) and also because they might not have thought of those possible clues and will work it in later on. Keep it wide and keep it open.
Some possible specialties include: crime scenes, forensics, interviews, leads, research, laws, prints, blood spatter, interview procedure, clue maps.
So what can you do with this skill?
Secure a crime scene (Wits + Investigation)
Search for footprints (Wits + Investigation)
Compare prints to shoes (Wits + Investigation)
Compare fabric and hair (Wits + Investigation)
Ask the right questions to a suspect in accordance with police procedure (Manipulation + Investigation)
Preserve the chain of evidence (Intelligence + Investigation)
Discover and lift fingerprints (Intelligence + Investigation)
Know what forensic scientists can do (Intelligence + Investigation)
Take crime scene photographs in accordance with proper procedure (Intelligence + Investigation)
Discover links between evidence (Intelligence + Investigation)
Brainstorm different avenues of investigation (Intelligence OR Wits + Investigation)
Search through a person's trash for clues to their lives (Wits + Investigation)
Examine injuries for a vague understanding of the cause (Intelligence + Investigation)
Apply human investigative strategies to occult phenomenon (Wits + Investigation)
Identify diagnostic equipment (Intelligence + Investigation)
Discredit evidence (Intelligence OR Manipulation + Investigation)
Call testimony into question (Intelligence OR Manipulation + Investigation)
Scramble witness memories the mundane way (Manipulation + Investigation)
Construct a map of events (Intelligence + Investigation)
Determine is a suspect's story matches the evidence-based timeline (Intelligence + Investigation)
Figure out ways of dealing with being investigated (Wits + Investigation)
You can find the core article with all of the other likely links over here.