We'll start with the Tesla. 1) look for unusual spots or an empty area with Walls around it. 2) if the empty area or bulge is 2x2 or 2x3 then there's a Tesla. 3) Be careful, as a player can try to deceive attackers by placing random bulges around their village.
To spot/set off traps safely: 1) have a few Barbarians when using this tactic. - for example, when attacking an undefended Town Hall: use a few Barbarians and place them in a circle around the Town Hall. This should set off any Teslas or Traps. if there is a Tesla, throw in a Giant and then Archers.
Giant bombs can cause devastating damage to all units. If there is an open area in a Wall 2x2 or bigger, use some Barbarians to find out.
Tip: Moving units can pass by any Trap without harm, except for Giants, Wizards, and Pekkas. But if a Bomb or Giant Bomb is within 1 tile of any building, the troops attacking that building will be damaged.
To spot an Air Bomb: Use 2 Balloons for this, as they will deal splash damage and additional damage when taken down. Send in all your troops, and if you have Healers, throw in the Balloons, then the Healers. That way the Balloons take the damage from any air Bombs or air defenses.
Seeking Air Mine: Minions don't work for this, as they will not be targeted. Send in a Balloon, then any available Dragons. That way, they'll be safe.