carbocation stability

Carbocation are highly reactive intermediate species, they have one an inherent positive charge and thus always in the look out for electrons, which tells us about their high reactivity. 
So the stabilization effects in a Carbocation are as follows: 
(1) Carbocations are stabilized by neighboring carbon atoms
Carbons (alkyl groups) are “electron-releasing” groups through inductive effects, thus stabilizing the system. The second is hyperconjugation, which stabilizes through donation of the electrons in C-H sigma bonds to the empty p orbital of the carbocation.

2) Carbocations are stabilized by neighboring carbon-carbon multiple bonds.
Any Double bond is a rich source of electrons, π clouds above and below having loosely attached electron cloud, this electron cloud, with the resonance effect can donate the electrons to the Carbocationic Carbon.This effect, called “Delocalization" where the charge “moves” from atom to atom. Delocalization of π electrons.

3) Carbocations are stabilized by adjacent lone pairs
The key stabilizing influence is a neighboring atom that donates a pair of electrons to carbocation. Note here that this invariably results in forming a double bond (π bond) and the charge will move to the atom donating the electron pair. Hence this often goes by the name of “π donation”.

4) Also Stabilized in presence of Polar Sovents, by solvating the carbocation species. This aids in increasing the reaction rate of the S1N reactions.

There are many factors,coming directly to the answer

1. Stability is directly proportional to the +I effect,that is the reason tertiary carbocation is more stable than secondary( explained by hyperconjugation or dispersal of charge)
2. Carbocation stability increases with increase in percentage of p character in hybridization
3. Carbocation stability increases with increasing alpha hydrogen atoms due hyperconjugation
4. Carbocation are stabilized by adjacent lone pairs of electron due to resonance
5. Carbocations are stabilized by neighbouring carbon carbon multiple bond due to resonance

There are 2 types of groups EDG (electron donating group) and EWG (electron withdrawing group).

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A carbonation is a centre of positive charge which will be stabilised when an EDG is bonded with it. This is known as +I effect of the EDG. Further it will be more stabilised when more number of EDG groups are attached. 

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Therefore the order of stability of carbonation is 3°>2°>1°.

How do I compare the stability of carbocation depending upon -

1. Hyperconjugation more the hyperconjugation more the stability of carbocation. This seen in 3° carbocation.
2. +I effect more the electron releasing group attached to carbocation more the density of electron increases on the carbocation so stability increases. So 3° carbocation is more stable.
3. +R effect group donate the lone paire to the near carbocation and stable the carbocation. So tripheny carbocation is more stable.
4. So stability order is 3°>tripheny carbocation> Allylic carbocation >2>1.
5. But most stable is tricyclo propane carbocation due to bend p- orbital of cyclo propane.

The general stability order of simple alkyl carbocations is: (most stable) 3o> 2o > 1o> methyl (least stable)

This is because alkyl groups are weakly electron donating due to hyperconjugation and inductive effects. 
Resonance effects can further stabilise carbocations when present (therefore allyl or benzyl carbocations are more stable than simple primary carbocations).

the stability of carbocation is decided by following factors = dancing resonance are most stable > part of aromatic system > +M stabilised > +H stabilised > +I stabilised > -I unstabilised > -H unstabilised > -M unstabilised > part of antiaromatic system

Note -i assume you know all these effect