To truly understand RedOx and Oxidation States (O.S.), you need
to understand about Electronegativity, and be able to draw out the
Kekule structures of the compounds (to see for yourself how
electrons in such-and-such a number of bond pairs, are
polarized and drawn away from the less electronegative species
toward the more electronegative species; to make sense of the
MEANING of Oxidation State).
However, because at 'O' levels you're not taught about these, it
then becomes an issue of oversimplified principles, blind faith,
and "just memorize, don't ask so much" pedagogical
limitations.
Assuming you're 'O' levels then, I'll just give the simplified
explanation and you'll just have to do your best to work
with it.
Reduction and Oxidation is primarily a matter of electrons,
gaining and losing electrons. Oxygen is often used to define redox,
simply because oxygen is the 2nd most electronegative element
(after F), and the Redox definition of losing and gaining oxygen
works in virtually all contexts.
The mistake you made, in thinking that the oxidation state had
actually increased from -2 to +3, is due to the fact that you
can only specify the oxidation state of (atom(s) of) an ELEMENT in
a particular compound, and not the compound itself.
That's right. You CAN say the dichromate(VI) ion has a
CHARGE of 2-, but you CANNOT say the dichromate(VI) ion has an
oxidation state of -2.
You can ONLY say, the oxidation state of CHROMIUM (the element)
has decreased, from +6 (in the dichromate(VI) ion) to +3 (in the
chromium(III) ion).
Hence, in terms of electrons, the (atom(s) of the) ELEMENT in
the compound has GAINED electrons when going from
the LHS (ie. the dichromate(VI) ion), to the RHS (ie. the
chromium(III) ion).
In terms of oxygen, the COMPOUND on the LHS (ie. the
dichromate(VI) ion) has LOST oxygen to become the compound on
the RHS (ie. the chromium(III) ion).
>>> I also do not know how you see that oxidation
state of chromuium decreases from +6 to -3. <<<
For 'A' levels :
Draw the Kekule structure of the dichromate(VI) ion, note
the number of bond pairs each chromium atom shares with oxygen
(ie. 6), realize that in each bond pair, the electrons are
polarized toward the more electronegative oxygen and hence each
chromium atom has 'macham' lost 6 electrons; then compare it to the
(obvious) oxidation state of +3 in the chromium(III) ion.

(Image owned by and courtesy of http://pubchem.ncbi.nlm.nih.gov )
For 'O' levels :
1. The oxidation state of oxygen is -2 (it's always -2 except in
the case of either bonded with lagi electronegative fluorine
(whereupon F gets priority of -1 to achieve stable octet, and
O.S. of oxygen is variable), or in the case of peroxide ion
-O-O-; since oxygen kakilang, oxygen equally electronegative with
oxygen, so they won't bully themselves, so each share the
electrons in the bond between the 2 Os equally, so O.S. of oxygen
is -1 in peroxide ion)
2. Let the oxidation state of Cr be X (algebraic variable).
Hence (2)(X)+(7)(-2)=-2; X = +6.
3. Hence oxidation state of Cr on LHS is +6, on RHS is
+3.
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