Engineers are characters in Elite Dangerous that can make modifications to almost everything you can add to your ship; hard points, utilities and internal modules.  There are some exceptions, but not many.

When you start playing Elite Dangerous you will have 5 engineers in your list.  As you level up each engineer in your list, you will discover new engineers.  There are 20 in total and all require different actions to be taken in order to unlock them for use.  The first two engineers you should unlock are Felicity Farseer and/or Elvira Martuuk as these engineers can increase the jump range of your Frame Shift Drive.

All engineers are located on planet surface bases therefore you need the Horizons DLC to access them.

The Elite Dangerous Wiki has more information on the engineers available to unlock;  who they are, where to find them, how to unlock them, etc.

Click on image if you'd like to know more.

The Engineers

Elvira Martuuk

Travel 300ly from start
Provide 3t Soontill Relics

Frame Shift Drive 5 Fast Charge or Long Range
Shield Generators 3
Engines & Thrusters 2
Shield Cell Banks 1

Felicity Farseer

Exploration rank Scout
Provide 1t Meta-Alloys

Frame Shift Drive 5 Long Range or Fast Charge
Engines & Thrusters 3
Shield Boosters 1
FSD Interdictor 1
Power Plants 1

The Dweller

Use 5 black markets
Pay 500,000 credits

Power Distributors 5 Charge Enhanced
Pulse Lasers 4
Burst Lasers 3
Beam Lasers 3

Tod "The Blaster" McQuinn

Earn 15 bounty vouchers
Provide 100,000 worth of bounty vouchers

Multi-Cannons 5 Efficient
Rail Guns 5
Fragmentation Cannons 3
Cannons 2

Liz Ryder

Befriend Eurybia Blue Mafia
Provide 200t landmines

Missiles 5 Capacity
Torpedos 5
Mines 3
Hull Reinforcement 1
Armour 1

Zacariah Nemo

Elvira Martuuk grade 3-4
Befriend Party of Yoru
Provide 25t Xihe Companions

Fragmentation Canons 5 Efficient
Multi-Canons 3
Plasma Accelerators 2

Juri Ishmaak

Felicty Farseer grade 3-4
Earn 50 combat bonds
Provide 100,000 worth combat bonds

Sensors 5 Lightweight
Detailed Surface Scanner 5
Mine Launcher 5
Missiles 3
Torpedos 3
Frame Shift Wake Scanners 3
Kill Warrant Scanners 3
Manifest Scanners 3

Lei Cheung

The Dweller grade 3-4
Traded with 50 markets
Provide 200t gold

Shield Generators 5 Thermal Resistant
Sensors 5
Detailed Surface Scanners 5
Shield Boosters 3

Selene Jean

Tod "The Blaster" McQuinn grade 3-4
Mine 500t ore
Provide 10t painite

Hull Reinforcement Packages 5 Heavy Duty
Armour 5

Hera Tani

Liz Ryder grade 3-4
Empire rank outsider
Provide 50t kamitra cigars

Power Plants 5 Overcharged
Detailed Surface Scanners 5
Sensors 3
Power Distributors 3

Marco Qwent

Elvira Martuuk grade 3-4
Befriend Sirius Corporation
Provide 25t Modular Terminals

Power Plant 4 Low Emissions
Power Distributor 3

Colonel Bris Dekker

Juri Ishmaak grade 3-4
Friendly with federation
Sol permit
Provide 1,000,000 worth combat bonds

Frame Shift Drive Interdictor 4 Expanded Arc
Frame Shift Drive 3

Ram Tah

Lei Cheung grade 3-4
Explorer rank surveyor
Provide 200t classified scan databanks

Heat Sink Launchers 5 Lightweight
Point Defence 5
Electronic Countermeasures 5
Chaff Launchers 5
Collector Limpet Controllers 4
Prospector Limpet Controllers 4
Fuel Transfer Limpet Controllers 4
Hatch Breaker Limpet Controllers 3

Didi Vatermann

Selene Jean grade 3-4
Trade rank merchant
Provide 50t lavian brandy

Shield Boosters 5 Heavy Duty
Shield Generators 3

Broo Tarquin

Hera Tani grade 3-4
Combat rank competent
Provide 50t fujin tea

Pulse Lasers 5 Efficient
Burst Lasers 5
Beam Lasers 5

Professor Palin

Marco Qwent grade 3-4
5,000ly from start
Provide 25t thargoid fragments

Thrusters 5 Dirty Drives
Frame Shift Drives 3

The Sarge

Juri Ishmaak grade 3-4
Rank midshipman with federation
Provide 50t aberrant shield pattern analysis

Rail Gun 3 Capacity
Cannon 5
Collector Limpet Controllers 5
Prospector Limpet Controllers 5
Fuel Transfer Limpet Controllers 5
Hatch Breaker Limpet Controllers 5

Lori Jameson

Marco Qwent grade 3-4
Combat rank dangerous
Any rank elite
Provide 25t kongga ale

Life Support 4 Lightweight
Detailed Surface Scanners 5
Sensors 5
Refinery 4
Fuel Scoop 4
Auto Field Maintenance Unit 4
Frame Shift Wake Scanner 3
Kill Warrant Scanner 3
Manifest Scanner 3
Shield Cell Bank 3

Bill Turner

Selene Jean grade 3-4
Friendly with alliance
Alioth permit
Provide 50t bromellite

Detailed Surface Scanner 5 Fast Scan
Sensors 5
Plasma Accelerators 5
Life Support 3
Refinery 3
Auto Field Maintenance Unit 3
Fuel Scoop 3
Frame Shift Wake Scanner 3
Kill Warrant Scanner 3
Manifest Scanner 3

Tiana Fortune

Hera Tani grade 3-4
Friendly with empire
Provide 50t decoded emission data

Kill Warrant Scanner 5 Fast Scan
Frame Shift Wake Scanner 5
Manifest Scanner 5
Collector Limpet Controller 5
Prospector Limpet Controller 5
Fuel Transfer Limpet Controller 5
Hatch Breaker Limpet Controller 5
Sensors 5
Frame Shift Drive Interdictor 3
Detailed Surface Scanner 3

Note:  The pins shown above are only a guide to help decide which blueprints to pin

Dav's Hope / Hobbes Hope

Dav's Hope can be found on the planet Hyades Sector DR-V c2-23 A5 at the coordinates 44.818, -31.389

You can farm the following materials there;

chemical distillery, chemical manipulators, chemical processors, compound shielding, conductive ceramics, conductive components, conductive polymers, configurable components, electrochemical arrays, flawed focus crystals, focus crystals, galvanising alloys, grid resistors, heat conduction wiring, heat discretion plate, heat exchangers, heat vanes, high density composites, hybrid capacitors, mechanical components, mechanical equipment, mechanical scrap, phase alloys, polymer capacitors, refined focus crystal, salvaged alloys, shield emitters, shielding sensors, worn shield emitters

You can also get the following data from the Data Point;

cracked industrial firmware, classified scan databanks, specialised legacy firmware, tagged encryption codes, unusual encrypted files