I know a lot has already been said by many who are clearly intensely passionate about this subject, but I just have this to offer to the OP in regards to his question:
To summarize what everyone has said, you have to do things the old fashioned way if you get lost in the woods with your radio and the only repeater you can reach is USFS.
You have three options:
A. Hike yourself out.
B. Wait to be found (maybe put some sticks together in a big X, since lighting signal fires would be ill-advised.)
C. Die of exposure, starvation, or dehydration.
This is, of course, if you don't have a satellite device of some kind, but what's the fun in that? Not everyone is made of money.
Might as well stay at home ¯\_(ツ)_/¯
Actually, staying in one place, i.e. option 2 is recommended in nearly every document about getting lost, traveling in wildland areas, etc.. It is the basis of the "Hug a Tree" campaign for young children. Signal fires have sometimes cost a few million to tens of millions to put out. It is better to use rocks to spell out "help." Sticks are not visible enough. A SPOT device costs about $200-225. A network service plan costs about $25/year. This is less than the equipment a person should be carrying when backcountry skiing, which includes a shovel, avalanche beacon, probes, avalanche assessment tools, a minimum 3 day avalanche training class, clothing layers, boots, skis, poles, goggles and anything I've forgotten now that I'm old and have limited mobility. The SPOT device also has map features and GPS that are useful all the time, not just for emergencies. Hiking costs far less than many other activities. I think of my $3200 carbon fiber road bicycle when I started to get serious about cycling as a exercise. I think about the cost of a pickup and just a shell camper, a RV, a boat, ham radio equipment, downhill skiing, boats for fishing or water skiing, fly fishing, snowmobiles, motorcycles, ATV/UTV's etc. Getting the best equipment for day hiking and backpacking is not cheap, but the startup costs are far lower than those other activities. If a person is able to afford the best and most durable equipment it can last decades without replacement. SPOT devices can save lives, not only your own, but the lives of people you might come across while hiking. That SPOT device in those circumstances is priceless.
I also recommend people carrying some type of fabric that contrasts with the ground and vegetation in the area a person is going hiking in. I carry an emergency poncho that is blaze orange. That doesn't work well in the slickrock country of southern Utah and northern Arizona where the predominant rock and soil is a reddish and orange color, so I also have a bright blue space blanket for those circumstances. I almost always carry a wool sweater and full Gore-Tex gear (parka and pants) on nearly every day hike and all overnight hikes. I carry the layer I know I absolutely don't need on a hike, that way I have what I need when things happen and they do if you are outside enough. I also carry a compass with a mirror for sighting the direction while looking through the "sight." It makes a great signaling mirror for aircraft. If a person does not know how to use a compass and map, they should not be hiking. Check the "ten essentials" for outdoor travel and always include those in a pack, along with other items depending on the location and climate.