[This applies to Canada, more specifically Ontario]...In a situation like this, you should take the following actions:

1) realize that you are not obligated to speak to the police, though it is probably a good idea to respond to their questions and be respectful;
2) if you have just been walking along and the police start to talk to you, they have the power of 'investigative detention', i.e. they are briefly allowed to stop, question, and pat-down frisk you if they are investigating a crime and you fit the suspect's description, i.e. they are allowed to ascertain your identity.
3) whenever the police say they want to search you (or your vehicle), tell them you are refusing to give your consent to perform the search...they are allowed, like I said earlier, to do a pat-down search, but unless you are being arrested (a search incident to arrest), they cannot go further than that. As for vehicles, if you refuse consent they cannot perform a search without arresting you.
4) politely ask the officer(s) why they are interrogating you and be sure to ask them whether you are being placed under arrest, and if you are not, ask if you are free to leave.

BTW, always keep this in mind, the SCC has ruled that the police are NOT entitled to perform 'random virtue testing', i.e. they are not allowed to interrogate an individual without the requisite grounds.

if anyone has any q's, I can try to respond with adequate answers.