Multimeter
Your first tool is going to be your multimeter. This is used to measure Current (amps), Voltage (volts), and resistance (ohms). It will be tempting to go for the cheap one because you are just starting out, but I find these unreliable and they just don’t last like the ones that are just a bit more expensive. I would recommend either of these to the beginner:https://www.amazon.com/gp/offer-listing/B00BRKYL7A... (heres a guide to buying one:http://multimeter-test.com/multimeter-buying-guide...) We use this to check if a circuit has connectivity, or if there is a break in the wires, and whether or not the individual parts are working, as they should. A nice example of using it to measure whether or not there is connectivity would be when I was trying to fix my ¼” jack cable for my electric guitar. The signal would sometimes lose connection, so I checked each individual part of the jack’s ends to see if they were all good, because if not that meant the cable was broken somewhere, and there was just a break in one of the solder joints. I quickly soldered it together and it worked perfectly from then on.
Soldering Iron
Speaking of soldering, if you plan on making circuits on more than just a prototyping board, you’re going to need a soldering iron. For a soldering iron, when buying one, I would suggest one with controlled temperature; when you start getting into more technical designs, some components will expire if the temperature is higher than it can handle. Also, right out of the box, when you first use it you should tin the tip of the iron. This is just the process of getting a little bit of solder on the tip before you begin soldering. I would try and avoid cheap ones with only one setting, but this is the one I currently use with different tips https://www.amazon.com/gp/offer-listing/B000BRC2XU.... and another with a bundle https://www.amazon.com/gp/offer-listing/B00AWUFVY8.... Oh yeah, and you’ll probably want to buy a roll of solder with this one.https://www.amazon.com/DMiotech®-0-8mm-Rosin-Solde...
Helping hand anyone?
A good thing to have when soldering together boards would be a set of "Helping hands." How you get these really depends on you, but I would avoid small flimsy ones, as a sturdy one feels better, has more resistance when you put the iron against the board, and won’t feel like you’re adjusting it every time. You can either make these yourselves, or buy them online or at an electronics store. I personally prefer this design, http://www.instructables.com/id/Helping-Hands-Sold... as its relatively easy to make, customizable, and most of all, cheap for just starting out.
Suck that solder!!
You’re bound to make mistakes, so having a solder sucker, or copper wire braid to clean up the messy solder joints are a good idea. I remember when I first got the solder sucker after going at circuits for a long time without, it felt amazing to just erase the mess and start over. https://www.amazon.com/Nulink™-Deluxe-Desoldering-...
Now that you have the tools for most of the work, it’s just the odds and ends you pick up that are more tailored to what you need. Within the first few projects you will probably get wire cutters, wire strippers, and a set of screwdrivers.
I need more powwwwweeeerrr!!!!
Other than that, when I first got started, my absolute first project, was a bench top power supply. The benefits of having a bench top power supply that you can plug into the wall, is that you don’t have to rely on your stash of batteries to power whatever it is you are working on. Later down the line, you can use it to recharge re-usable batteries, test circuits, and power some gadgets. If you can afford one (unlike me at the time), then great, otherwise a quick Google search will send you to an innumerable amount of schematics, or pc power supplies that you can convert (be sure to be extra careful when dealing with mains AC voltage, which is the electricity that comes out of a wall socket). This is a good project I think, because it teaches you to be very cautious when dealing with electricity, and that it is important to read diagrams and learn about the projects more in depth, before diving in.
Oscillo-what?
The next advanced piece of equipment, which I find useful for testing more complex circuit boards, is an oscilloscope. This is used to search for anomalies in circuit boards performances, and to work with AC voltage, or signals from devices. Like I said, this isn’t essential to those just testing the waters of working with electricity, especially at the price point they are at, at around $300 for a good one, but it will be something you will need if you decide to take on harder tasks.
Don’t let any of these overwhelm you though, because often more than not, some simple circuits are already put together for you, and just searching online for what you need will save you the trouble of reinventing the wheel.
You got this!!!
Now that we’ve got the basics of what these things do, this will make it easier to understand how we can accomplish analyzing a circuit and making you’re own!