Ravana abducted Sita towards the end of 13th or early part of 14th year of her, Rama and Lakshmana's exile from Ayodhya. There are several references in Valmiki Ramayana to support this fact.
In Aranya Kanda, Sarga 16, Valmiki mentions the ṛtu (season) as Hemantha (late-autumn or pre-winter, Mārgaśīrṣa or Pauṣa month):
vasatastasya tu sukhaṅ rāghavasya mahātmanaḥ.
śaradvyapāyē hēmantaṛturiṣṭaḥ pravartata ৷৷3.16.1৷৷
While the great self Rama lived happily there, autumn passed and dear winter set in.
And later in Aranya Kanda, Sarga 56, Ravana, soon after abducting Sita, warns her that she only has an year to change her mind and marry him:
śṛṇu maithili madvākyaṅ māsāndvādaśa bhāmini ৷৷3.56.24৷৷
kālēnānēna nābhyēṣi yadi māṅ cāruhāsini.
tatastvāṅ prātarāśārthaṅ sūdāśchētsyanti lēśaśaḥ ৷৷3.56.25৷৷
O comely princess from Mithila, O lady with a sweet smile! listen to my words. If you do not accept my hand in the course of twelve months, the cooks will cut you off into small bits for (my) breakfast.
In Sundara Kanda, Sarga 58, Sita tells Hanuman that she's only 2 months left before Ravana would kill her:
yadyanyathā bhavēdētaddvau māsau jīvitaṅ mama.
na māṅ drakṣyati kākutsthō mriyē sāhamanāthavat ৷৷5.58.106৷৷
Otherwise with none to protect me, I will live only for two months. I will die like an orphan and he [Rama] will not see me.
Then it took Rama and the vānarās a couple of months to build the Nala-setu, reach Lanka and finally defeat Ravana in the Phālguna month, an year after Sita was kidnapped. Rama frees Sita immediately after Ravana is killed and then they all head back to Ayodhya after the 14-year exile.
One particular attempt at astronomically dating the Ramayana, provides the following timeline for some major events of Ramayana:
Rama's Birth Date 4th December 7323 B.C
Rama-Seeta Married 7th April 7307 B.C
Rama Exiled 29th November 7306 B.C.
Hanuman enters Lanka 1st September 7292 B.C
Hanuman meets Seeta 2nd September 7292 B.C.
Setu (Bridge) built 26-30th Oct. 7292 B.C
on the ocean
The War begins 3rd November 7292 B.C
Kumbhakarna is killed 7th November 7292 B.C.
Ravana is killed by Rama 15th November 7292 B.C.
Rama returns to Ayodhya 6th December 7292 B.C.