General Guide : Invisibility

Sentry Ward

Stationary and 100gold a ward. Last 4mins. Good in laning stage to zone an invisibility offlaner like Bounty Hunter, Broodmother, Clinkz,... Better as a defensive item than offensive. Good choice if they can purge or remove Dust of Appearance somehow.

Dust of Appearance

Best as an offensive item. Tracks and slows the hero while in invisibility. 75 gold a charge. Can be removed through various means like purge, Dark Pact, Time Lapse, Press The Attack,...  Generally used to gank a hero who can invis to escape/juke.

Gem of True Sight

One of the more expensive items but deadly early. Good to deward and good as defensive and offensive. Lands on ground when the holder dies. Often swaps between teams or until one leaves it at base. Learn when to buy this and it can completely shut down some heroes winning you the game. The range isn't quite as safe as having Sentry Ward farther out.

Necronomicon Level 3

Around 5200 gold  for the level 3, the warrior carries the true sight. More of a bonus if you're getting necro than a good detection option

Situations where you use detection

Dust of Appearance to gank Riki, Clinkz. Beware Riki can purge himself of Dust of Appearance with Diffusal Blade which is common on him. It goes on cooldown for a bit so you can't reapply it quickly on say Weaver who ulted. If 2 people have it you can.

Sentry Ward in lane to zone Bounty Hunter. Can be placed to deward or to protect against scouting from invisibility heroes. Great against Moonlight Shadow from Mirana. Important against Nyx Assassin. Used to make an area safer, similar to a tower.

Gem to deward if you're not sure where their wards are. You can buy a Quelling Blade to kill the ward if you're a melee support hero. Also good like a mobile Sentry Ward. Can be dangerous to buy if you die often.

Necronomicon: similar to Gem, best to chase invisibility heroes and deward with. Can be like a Sentry Ward if you're using them to push.

To help with your situation

Generally newer players have problems not so much with buying detection but in map awareness. They lack the pro-activeness to get Dust of Appearance if you want to gank or zone an invisibility heroes in lane. It's just another skill to learn that takes time and failed games. Use pings and chat wheel to try to lead your team. Place Sentry Ward if you're pushing and defending. Bring Dust of Appearance or Sentry Ward to gank. Detection is important in team fights as well so when Riki / Bounty Hunter gets low they can't duck away and try to pick someone off who's running to base.

Invisibility is generally used to scout without the enemy knowing, gank without the enemy knowing, or to run away without being followed/targeted.

Your team mates are being ganked with the invisibility early on. I suggest get Sentry Ward for them if you can. If you know they're out of position, counter gank. This can be done by just guarding them so its 2  v 1. It can be done by hiding some distance off and waiting for the hero to gank your ally. Then Dust of Appearance, use Sentry Ward and go on the hero. Disables are important to keep the invisibility heroes locked down under a Sentry Ward or in sight with Dust of Appearance on.

If its happening before or during a fight. Sentry Ward are best here as defensive items during a push. You can extend the tower sight range in a way so you're not blinked on under tower or in base. If you're pushing place Sentry Ward so they can't wrap around and initiate on you.

A final note is that invis if countered makes the hero weaker. They now can only use 3 abilities effectively. If it's Shadow Blade, they wasted a bunch of gold that now only gives them attack speed and some damage. It feels unfair early on but Shadow Blade is a pretty crap item. It's only used in niche situations at the pro level and at higher MMR.