How do I fix a slow sink faucet?
From my one experience fixing a slow-running sink, I'd recommend these steps, weighted by likeliness to be the source of the problem and PITA-factor in troubleshooting:


Check other sinks.
Verify your shutoff valves under the sink are all the way on. Typically an on valve points in the direction of outgoing flow. If it's not clear, lefty tends to be loosey.
Check if you get the same issue turning the sink to all the way cold vs. all the way hot. Basic sinks are unlikely to have pressure/thermostatic balancers.


If the problem is imbalanced, it's at or before the mixing cartridge and unlikely to be in the flex hose or aerator/flow restrictor. Check hot/cold feeds first in following steps.
If the problem is balanced, and you're sure you don't have a balancing mixing cartridge, the problem is at or after the mixing cartridge and unlikely to be in the hot/cold feeds.
If the problem is balanced, and you're not sure what sort of hot/cold mixer you have, just continue.

Plug your sink with a towel or stopper or grate and pop off the assembly and look for debris. There may be several small parts so be careful.
Extract and inspect the mixing cartridge which should be accessible from above. You may need Channellock/tongue-and-groove pliers for this to remove a screw-on retaining ring if you can't loosen it by hand.
Lay down a towel under your sink, turn off your two water supply shutoff valves, and start detaching and inspecting the under-sink hoses depending on the priority order established earlier. A typical one-hole faucet will have one hot and one cold hose carrying water up a copper pipe coupling, which will go up into the cartridge and then back down through a copper pipe that couples to the flex hose ( sometimes through a fat plastic coupling that includes its own flow restrictor) which leads into the flex hose that you pull out of the sink. Remember that the ends of the couplings and hoses often twist independently of the hose itself, so you don't have to do too many acrobatics to twist things into place. Things to look out for:


If you have a plastic coupling with built-in flow restrictors, they may be clogged and need replacing/removal.
The hot and cold feeds from the wall should have very high pressure. If they don't, you have piping problems and are looking at a bigger fix.
If any coupling is clogged, you may have to remove it.
Once the hot and cold feeds are disconnected, you can try blowing on the system in reverse in the hopes of dislodging something, but this may make some problems worse.