Fishing cable through finished walls is mostly about planning the route, making small access points, and using the right tools so you can work with the wall instead of fighting it. The first thing I would do is confirm the path from start to finish and make sure you are not crossing anything you should not, especially plumbing, existing electrical, or fire blocking. A stud finder with wire detection can help, but do not treat it like a perfect map. If the wall is insulated or has horizontal blocking, expect the job to take longer.
For a typical vertical drop, cut a small opening at the top or bottom of the wall where you can see the cavity. A low-voltage old work box opening is often enough if you are adding a new outlet or data drop. Once you have access, drop a fish tape, glow rods, or a weighted pull string down the cavity and try to guide it out at the other opening. Glow rods are especially handy in finished walls because they are rigid and easier to steer around minor obstructions than loose tape. If you hit a fire block, you may need to drill through it from one of the openings using a long flexible bit. This is one of the most common reasons a wall fish stalls halfway.
If there is insulation, patience matters more than force. Try to work the tool along the edge of the cavity rather than straight through the middle of the batts. Sometimes a shop vac with a string and a small plastic bag or foam earplug can help pull a line through a very open cavity, but that trick is less reliable in insulated walls. Once the pull string is in place, tape the cable to it smoothly. Keep the connection slim and stagger the conductors so it does not snag on the opening or any rough lumber. A little lubricant can help in tight runs, but do not use anything that could damage the cable jacket.
Another thing people overlook is code and cable type. If this is low-voltage cable, the process is easier, but you still want to keep it separated from power cable where required. If this is line-voltage work, the rules are stricter and the safest choice is to have a licensed electrician handle it. Also, if the wall has no accessible attic or basement path, sometimes the cleanest solution is to use surface raceway instead of making a mess trying to force a hidden route.
The biggest practical tip is to expect one failed attempt and plan for it. Drill slow, check both sides of the wall before cutting, and make your access holes as small and strategic as possible. If you have a helper, one person feeding and one person listening or guiding at the other opening makes a huge difference. A couple of careful holes and the right fish tool usually beats trying to muscle a cable through blind.