1) open field - depending on the situation if there isnt any stenches there yet i would say dig a long trench typ thing make sure its deep enough so they cant get out fill it up with burniable stuff and have a zombieque. if they are already there and there isnt a lot of theam than picktheam off one by one until secure.
2 forest- most forests borde fields so if you conquer a field and have your field secure you can double the security by the border of the field and forest
as for the others ill back to you on those gotta think a little
open fields: if you have ground cover you have to worry about crawlers if you are moving across the field while clearing it the best way would be to set up high ground, the top of a SUV or even a hunt blind up on stilts then call the zombies in and shoot them as they apear , the same with a forest call the zombies out to open ground and pick them off as they apear if you have to move through the forest three man teams with each team close enough for support and a drag team one or two members who follow behind and watch the rear in case zombies get behind the teams,
Fields offer too much open ground. The zombies would soon overwhelm you if the came in great numbers. Assuming you placed yourself in the middle of the field, they could come at you from any direction, swarm you, and eventually over run your position.
The best defensive position is one with limited access in and out. A small river valley with steep walls for instance. You position yourself on the high ground on the upriver side of the valley with a clear view down river. Maybe create a few obstacles by cutting down trees or knocking loose boulders, to create choke points and slow them down. Any time you can funnel them down to one or two shoulder widths, that decreases your chance of being over run. You can start by picking them off at a distance and then switch to closer range weapons as they near you. Just don't box yourself into a corner, and be sure to have an escape route.
You can also do similar things in cities using man made obstacles. Use terrain to your advantage, and choose a structure on some high ground to defend. Then use vehicles, fences, and other objects to funnel them down into choke points and kill zones.
Difficult questions to answer without more details. For the sake of this discussion, I'm going to assume the following: A) Z-Day's come and gone, the human race has survived, and now we're looking at taking back the land. B) I have access to 75-100 soldiers and access to whatever equipment I need.
1. Open Fields - Have a couple of helis drop napalm. If I don't have access to aircraft, then a Combine Harvester should do the trick.
2. Forest - Depends on the size of the forest, what lies on the boundaries of the forest, and how infested we believe it may be. If it's heavily infested, then I don't take it back. We burn it. Straight down to the ground. If we don't believe it's heavily infested, then surround the perimeter with motion detectors. Then divide it up into quadrants. Clear out a quadrant at a time (quadrant size determined by the number of men available, working in groups of two, with all groups maintaining visual contact with at least two other groups at all times.) Drop more motion detectors through the quadrant.
3-8. Building by building, block by block, again with motion sensors placed throughout each section. Once a quadrant is clear, you fortify. Do not move onto the next quadrant without having a fully secured and fortified fall back location.
8) Realisticlly, I see absolutley no practical way to clear out 150,000+ zombies in less than a day
Since it is a large city though, it would have weapons, supplies (assuming they are not already looted by other survivors), and things that you could use to make fortifications. In order to even start a viable offensive campaign against these kind of odds you would need to get into the gun shops and get weapons and ammo, supply shops to get food and water (along with any other handy supplys such as matches, gasoline, personal items, toiletries, and other such things. but only to the extent of what you need)
ALSO, you would need to get into places such as home hardware or places that sell things like tools, sheet metal, blow torches, and other building supplies. Then you would need to find a viable shelter that is already defendable by itself without modifications (it will take some time to get fortifications in place and you might need to fend off zombies a couple times in the building process) and take up residence there. You would need to put blockades up and reinforce things such as windows so they could not get inside if they attacked. You may also want to consider a fall back point/escape route if things get too ugly. But all details aside (As I'm sure you get the picture) this would serve as a place where you could sleep, eat, fall back to and defend, and be otherwise secure from the hordes of slavering freaks outside. This is the most importent step, as clearing out 150,000+ zombies in less than a week is just unrealistic if you are alone.
Once you have a fortified position as described above, then you can start an offensive campaign to clear out the city. Just to get it out of the way, going rambo and attacking huge hordes of the things at once may well be the best way to get yourself killed. Instead, lure them into some sort of situation where you are at a ridiculous advantadge.
An example of this might be making as much noise as humanly possible to attract plenty of them to your fortified position, where they cannot gain acess to. Since you are safley inside, pick them off with the firearms previously gained and any other suitable weapons. Using this tactic you can kill large amounts of zombies in a single day. Unfortuneatley clearinf out over 150,000 plus zombies will not take a single day and will most likely reuquire repeating the above process a few times at least.
After a while however, this tactic may stop working as you may have killed all the zombies that are within hearing range, and assuming they do not come to you either because they somehow know you are there or because they want to eat the other zombie corpses that litter the outside of your position, then you will have to go to them.
Once again however, rambo stlye against these kind of odds is not a good idea, so a good idea might be setting a trap in a different location and then luring the zombies into it somehow (making noise may not work, so an explosion or pile of corpses may do it. Pherhaps even a bit of your blood in a smashed vile will draw them).
An example of such a trap might be taking soaking an area in flammable liquid (such as oil or gas) and taking up an elevated position that overlooks the area. You put the bait (whatever it is) in the middle of it (make sure the area is sufficantly huge) and wait until a large number of zombies have gathered there, then set fire to the area using something like a flaming arrow, lighter, match of something else that will set it ablaze. assuming you have done this right, the zombies will burst into flames and die. A burning death may take a few minutes for a zombies, but due to the gas/oil, the fire will keep going and feeding off the flammable liquid and zombies until they are ash.
Note: MAKE SURE YOU BRING WEAPONS ALONG TO DEFEND YOUSELF in case you are discovered or you need to pick off the survivors of your trap. Things such as pits may also assist you if you place them in random intervals around the city and allow the zombies to fall into them, then burn them. Always go back to your fortified position before dark however, as you cannot see well in the dark and fighting would be harder. You will be safe in your fortifid position until the next day.
KEEP YOURSELF ARMED AND ARMOURED TO THE HIGHEST AVAILABLE STANDARD AT ALL TIMES IN CASE OF SUPRISE ATTACK.
Cleaing out the city may take a while, but if you use the above tactics it is feasible.
1) open fields- a group of people with adequately sighted rifles and alot of ammo can clear alot of ground since the open field makes it very easy to see the undead, but it also makes it easy for them to see you. also, there may be some tall grass and undead who have lost their legs can stay undetected behind those areas until its too late. so if there is no other option, travel slowly, watch the ground and listen for rustling or moans.
for number 5 go in and clear out a few buildings and put snipers on the roofs. Then make a lot of noise atrackting all zombies in the town. (make sure you are in a strong vieshle with gun slits and good armor so the worst that can happen is it gets tipped over) Park the viechle in the center of the snipers circle and begin the onslot. after all zombies apear to be dead, do a thurrow search of every building, sewwer, and subway before the area is able to be called safe.