Modern military doctrine on the attack (in conventional warfare at least) is based mainly on blitzkrieg (lit lightning war (I think)) which is where small well trained mobile battle groups penetrate the lines of your opponent/opponents, now there are two main ways in which this can be developed:
-Envelopment this is where slower often less well trained/equipped troops follow along to deal with the cut off troops who should (if it works) be demoralized, under supplied and also fragmented (due to cutting off from command structures), this is the original Blitzkrieg as developed by the British in plan 1919 and in the 1920's and 1930's with the experimental armored striking force (I believe that was its name though I may be off slightly (it might be the name of the American equivalent which was far less significant)) and perfected by the Germans in the early stages of WWII (who made the wonderful step of including Aeriel envelopment as part of their plans). This plan has problems as it is susceptible to counter attacks (as British and French armored attacks in the German drive for the channel ports showed) and also if the enemy doesn't collapse entirely due to the attack it is susceptible to counter envelopment (battle of the bulge and of course Stalingrad).
-Goal grabbing (as this method has no name that I am aware of I have named it such) this is where the army is made up of almost entirely of mobile forces and so the attack plan is a somewhat extreme form of Blitzkrieg in that there is little or no envelopment. Instead the mobile forces push towards goals as fast as they can in the hope that firstly taking these objectives will cause the enemy to surrender or at least drastically limit their ability to fight and secondly that the enemy is either too gormless or simply unable to cut the lines of supply. A good example of this is the US (and ally) during operation "Iraqi freedom" where the generals knowing the limited capabilities of the Iraqi forces (i.e. no ability to contest the air control (except from old fashioned ground based defense systems), technically obsolete armour and anti armour capabilities, no/highly limited (depending on who you believe) NBC equipment, obsolete communications, virtually no reconnaissance, etc, etc) and so were able to use this battle plan with little fear of a misfire (even then they came dangerously close). Basically everything thats a problem with envelopment is a problem here but more so, also it has the added problem of you must completely own the sky it will fail if the enemy has even the most limited ability to contest the air war.
Blitzkrieg is an incredibly dangerous method of warfare in that it is a huge gamble which if it goes wrong can lead to your best troops (both in training and equipment) being lost so I would only consider it if all the advantages were mine.
A far safer attack method is deep penetration (if anyone makes a joke about that they get hit with fish) a method developed and used by the Russians during WWII after they had a failed almost Blitzkrieg attempt during the war with the Fins. This holds some similarity with the envelopment method of Blitzkrieg but on a hugely larger scale (Blitzkrieg is lightning rapier thrust, deep penetration is a steam roller) and as such it matters far less that the advantages (except of course for numbers) are in your favour, Reconnaissance (your enemy can see you, well good the more troops they bring the more you can destroy, its a harder fight but we cannot have everything in this life), Air power (meh we have planes they have planes there are more of us then them so our air power is a larger force multiplier), technology (they can destroy 10 tanks for each of theirs we destroy, good job we have 20:1 in our favour), I could go on but I won't. A good example of this is Stalingrad (widely thought of as one of the greatest envelopment victories ever).
