I have loaded a neural network onto a Raspberry pi pico and I want to know how to connect it to the oscilloscope to measure its power consumption over time. I have the necessary components for wiring such as the breadboard, wires, and resistors but I am unsure how to connect everything. Thanks for your help!
In general, you should "use the proper tool for the job" - which, in this case, means you might try to find a tool that's better-suited to power measurement than an oscilloscope. Oscilloscopes, in general, measure voltage changes over time. Since power measurements require measuring both voltage and current (or being able to calculate current), you may find the oscilloscope awkward for making power measurements - unless you're lucky enough to have a full-featured scope (see @Gil's comment below).
There is another answer here that offers several alternatives for measuring power input to an RPi - they will also work for measuring power input to the Pico.
I would suggest that you first consider one of the many USB devices for this. They sit between the Pico's USB microB input connector and the USB cable you use to power it. You may find one with USB micro-b connectors; otherwise, you'll need adapters.
Let us know if you have further questions on this, but N.B. that you'll need to do your own shopping - the rules here don't support "shopping requests".
Easy, clamp the current probe around either the + or - power supply wires. If the trace is reversed remove the probe, flip and put back. You then place the scope vertical input on the + and the ground on -. Adjust appropriately and at this point the screen will give you current and voltage. If your scope has math functions you can program it to give you watts directly. If not multiply them, just be careful of the decimal points (they usually get me). The one I use to do this is an older model A Tek a MSO 4054. The current probes use a separate amplifier. The newer ones do not need the external amp. My scope is my most important almost-all-in-one tool. Mine is a bench model which if fine.
This solution will work with micro power devices to ultra large industrial loads, you just have to scale the probes. When mains are involved I always use a step-down transformer, all that I normally need to know is the turns ratio. You can figure that out with the scope as well.