LEDs have various forward voltages depending on the color and chemistry used to create them.
You have here a list of forward voltages for various led colors:
https://en.wikipedia.org/wiki/Light-emitting_diode#Colors_and_materialsSo for example, most red leds will have an average forward voltage of 1.7v , most yellow and orange leds will have a forward voltage of around 2.1v, and white or blue leds require around 3v
You can chain multiple leds (put them in series) as long as the sum of their forward voltage doesn't go above the voltage of your power supply. So for example, with a 12v power supply (a cheap wallwart adapter) you could have 12v / 1.7v = 7.05v , so basically 7 leds. With 3v leds you'd want to stick to maximum 4 leds.
You'd probably want to chain only 6 leds though, because if you make a very long string, you may not have 12v near the end of the string due to losses in the thin wires you're going to use , so better to leave some room.
Now it's not enough to just put them in series, because leds don't behave like incandescent light bulbs. if you just connect them to the power supply, they'll burn up.
You have to limit the current going through the leds to a reasonable value, and the easiest way to do that is using a simple resistor.
For 3mm and 5mm, most leds have a recommended current of maximum 20mA (0.02A) but really for a xmas tree, you won't need more than 10mA
you can determine what resistor to put in series with your 6 leds using Ohm's law formula - I'm going with 6 red leds and a 12v power supply but you can change the numbers... I'm going to limit them to 10mA because it's enough
the formula is like this : Voltage equals Current x Resistance or V = IxR
In your case voltage is the power supply voltage, minus the sum of the forward voltages of your leds. The current is the value you want to limit the leds at, which is 10mA (0.01A) in my example
So : 12v - ( 6 leds x 1.7v) = 0.01 A x Resistance ... and from this > Resistance = (12v - 6x1.7) / 0.01 = (12v - 6x1.7) x 100 = 1.8 x 100 = 180 ohm
This is actually a
E24 value which means it's very easy to find, but if you had come up with a different number, you can round up or down to the nearest E24 or E96 value - slightly smaller resistor value means a bit more current through the leds, bigger value resistor means a bit less current so slightly less bright .
Now you ca make your tiny strings of a few leds + resistor and then you simply connect them to your two wires (positive and negative of your power supply). Easiest would be to cut a bit of insulation on each of those two wires and solder your tiny string of leds + resistor between the two wires and then use heatshrink or electrical tape to cover the point where you made the connections.
edit: also if you don't want to spend money on a power supply but you have a phone charger or usb power bank or anything with micro-usb connector, you can buy one of these boards which have contacts for wires so that you could connect wires from a set of batteries like 4AA batteries for example, but they also have a micro usb connector, so you could plug a phone charger or usb power bank in them...
here's a couple of sellers
1:
https://www.ebay.com/itm/2A-DC-DC-Boost-Step-Up-Voltage-Converter-Micro-USB-2-24V-To-5-28V-Adj-Regulator/112931387130?hash=item1a4b3c36fa:g:h2kAAOSwHgday3gf:rk:1:pf:02:
https://www.ebay.com/itm/DC-DC-Boost-Step-up-Regulator-Converter-USB-2-24V-to-3-3-3V-5V-9V-12V-24V-Module/322369192609?epid=2118019319&hash=item4b0eb382a1:g:9EoAAOSwpqRazhQN:rk:2:pf:0So that can boost up to 28v but with just 5v at the input, it probably can't.
It can probably do 12 ..15v just fine, at up to around 1A ... and that would be just fine if you use a 5v 1..2A phone charger
Basically, if you use a 5v 1A phone charger, you have around 4.8w (because the tiny board isn't 100% efficient) at 12v , which means the maximum current would be 4.8w / 12v = 0.4A .. so if your strings of leds use 10mA each, then you could have up to 40 such led strings on your long string of leds ( so with my example of 6 red leds per tiny string, up to 240 leds in total)