How do you design a power supply for an LED strip if you do not have any specifications?
Judging by the pictures, your LED strip is composed of blocks of three LEDs in series with a resistor.  The blocks are in parallel to make up the length of the strip.
White LEDs need about 3V to light up.  With three in series, that's 9V. That leaves 3V to be dropped across the resistor.
The resistors in your photo are 150 ohm parts.
Using Ohm's law (\$ I = \frac {V}{R}\$,) we find that the current through the resistor will be \$ I = \frac {3}{150} = 0.02 amperes\$.
Since the resistor and the three LEDs are in series, the resistor current is also the current for the block.
Multiply 0.02 amperes by the number of LED blocks on your strip.  That's how much current your power supply must deliver.
Find a 12V power supply rated for that current or higher.  More won't hurt the LEDs, it'll just be more expensive.
Your LED strip is dimmable.  There's nothing in it but LEDs, resistors, and wire.

You can vary the current to dim it.
You can vary the supply voltage to dim it.
You can use pulse width modulation (PWM) to dim it.


For a more accurate estimate of the current, measure the forward voltage of one of the LEDs.  White LEDs usually use a blue LED with a phosphor coating to make white.  Blue LEDs usually have about 3V as a forward voltage, but some are lower.  I have a bunch here with 2.5V forward voltage.  That would change the calculated current from 0.02 to 0.03 amperes.

I find 12V DC constant voltage dimmable power supplies available from various places with various power (current) ratings and for various prices - up to eye-wateringly expensive.
Look around, see what you can find.