The great detective...

This information is going to help you be a detective. Use this information wisely and use it only for the right reasons.

[edit] Steps

Be yourself. When spying, act like a relaxed normal person; you don't have to wear dark shades and a trench coat to be a spy. You need to blend in; just be another face in the crowd.
Carry around a camera at all times. There's always something interesting happening.
Be smart when following people. Don't follow too closely behind and don't look into shop windows every time they turn around, just keep walking. Even if they do spot you, someone walking down the street looks more natural than one constantly hopping into alleys or stores.
Cultivate an eye for detail. Make a habit of observing your surroundings, even when there is nothing in particular to observe. You never know what you might spot, and you'll be honing your skills.
Learn to read people's faces. Watch body language and notice whether it seems natural and agrees with their words.
Get good at searching for information. Learn what is a matter of public record and how to obtain it.
Practice asking questions. You should be able to get to the heart of a matter without putting somebody on their guard or making them uncomfortable, unnecessarily.
Keep careful notes of what you find.
Get yourself a kit. It should include a magnifying glass, binoculars, fingerprint dusting powder, etc.
If you can't buy a kit try to find somewhere that will tell you how to make a kit with items around the house

[edit] Tips

You are not a real detective unless you have a badge, any badge will do even a toy badge will work.
Detectives don't only solve crimes. Sometimes, they simply look for missing information.
Read detective novels (Sherlock Holmes, The Hardy Boys, Nancy Drew, Half Moon Investigations)
Watch detective shows or movies (for example: Law and Order, Veronica Mars, X-files, Monk)
Read detective comics (Batman, Dick Tracy, Crime Suspense Stories)
If you have a friend with you , always talk to them if the person sees you.
Cultivate a sense of minor paranoia, enough to sense danger, but not enough to act out in public noticeably.
Be cunning, try not to give the game away.

Always obey the law. Being a detective does not confer any special status.
You need to be careful in case a detective is spying on you.
Don't spy unless you are absolutely sure about the person's intentions.
Be careful. Someone you are spying on could be dangerous.
Always be prepared for anything.
Have at least two back-up plans, should anything go wrong.
Do not become a criminal yourself.
It's very useful to have a partner that you can trust.
Don't-- DON'T-- go around dressed up as 19th century Sherlock Holmes. You will look like a COMPLETE idiot.
NEVER EVER EVER do anything dangerous or potentially harmful- a REAL detective uses their common sense.