Where do I enter cheats, and what do they do?

Go to the Hub menu > Extras > Cheats to add and enable/disable cheats.

Here's the list of cheats in Saints Row IV:

• Unlock Infinite Sprint - runfast
• Unlock Telekinesis - supertk
• Unlock Stomp - superstomp
• Unlock Blast - superblast
• Unlock Buff - superbuff
• Unlock Death From Above - superdfa
• Disable Super Movement - nosupermove
• Disable Super Powers - nosuperpowers
• Elevator to Heaven (corpses rise into the air) - fryhole
• Give $100,000 - cheese
• Clear Notoriety - goodygoody
• Player Vehicle Smash (any player car will crush other cars like a tank) - isquishyou
• Repair current vehicle - repaircar
• Gives the following weapons (baseball bat, heavy pistol, heavy smg, semi-auto shotgun, automatic rifle, alien rpg and the mcmanus 2020) - letsrock
• Give alien hover vehicle - givehovercar
• Give alien hover tank - givehovertank
• Give alien ufo - giveufo
• Unlock all unlockables - unlockitall
• Fast Forward - fastforward
• Give XOR (alien hoverbike) - givetrouble
• Give Monster Truck - givemonster
• ASCII Mode - ascii
• Disable Warden spawns - nowardens
• Instant Warden Notoriety - instantwarden
• Mascot Peds - mascot
• Pimps and Hos Peds - hohoho
• Insane City - insanecity
• Evil Cars - evilcars
• Disable Glitch FX - noglitchcity
• Big Head Mode - bigheadmode
• Invincible Player Vehicle - vroom

Executive Privilege Pack DLC cheats

• Your vehicle has infinite mass and smashes other vehicles out of the way - dlc_car_mass
• You will never die - dlc_never_die
• Unlocks and purchases all Super Power Upgrades - dlc_sosuper
• Maxes out Super Power Strength - dlc_superduper
• Gives you infinite ammo for all weapons - dlc_unlimited_ammo
• You never have to reload because your clip runneth over forever - dlc_unlimited_clip

^{Sources: "Additional Cheats (SR4 mod)", Saints Row Mods | "Cheats in Saints Row IV", Saints Row Wiki}

I can't earn achievements because my partner was using cheats.

If you're playing the PC version, you'd probably want to install the Additional Cheats mod (for your SR4 installation and the people you're playing co-op with). Description:

This mod adds 160 new cheats to the game, as well as changing all cheats to non-flagging... That means using them will no longer disable your autosave or achievements.

As I am unsure what kind of Gaming Platform you are using I will list out both PC and Xbox360/PS3. For XBox360 cheat codes, you can go to this site

To activate cheat mode, pause the game, and select "Extras" and "Cheats". Select "Add Cheat" and enter one of the following codes to activate the corresponding cheat function. If you entered the code correctly, you will hear a sound.

As for the list of Xbox360/PS3 cheats that I currently know of: (I did not add the world codes etc. as you can find these in the website I gave)

•cheese - gives you $100,000

•letsrock - gives you a full set of weapons

•runfast - you can sprint forever

•whatitmeanstome - give respect

•brains - zombie mode

•ammojocky - toggles unlimited ammo

•vroom - your vehicle is immune to damage

As for the PC version, you can check out this website

You can enter cheats by accessing the HUB menu, then the Extras menu, and finally the Cheats menu. Entering codes disables auto-saves and also will not allow you to earn any in-game Trophies or Achievements unless you load a save without the cheats enabled. You can enter any cheats below to access the corresponding effects

•cheese - Puts $100k in your pockets (can be spammed multiple times in a row)

•letsrock - Gives you a full load-out of randomized weapons

•goodygoody - Removes the Notoriety from you at any time

•runfast - Your super-sprint doesn't exhaust your Stamina

•fryhole - All of the dead bodies lying around start to raise up into the air

•vroom - Indestructible cars

•isquishyou - All cars can now drive over other cars like tanks (can only be turned off by reloading a clean save)

•hohoho - This makes all of the pedestrians either pimps or prostitutes (LOVE THIS ONE)

•mascot - All pedestrians turn into mascots

•evilcars - Makes all of the cars on the road target you and start attacking you