How does a miner put his vote for certain BIP? I understand that a miner is the only one who can vote for a certain BIP, but I'm wondering, how do they technically do that? How do they submit their vote? I found out that they  are doing it through the coinbase transaction, but I couldn't find any details on it. 
Thanks!
See my answer here to address some of your misconceptions. TL;DR: miners signal support in blocks for certain rule changes in order to coordinate activation, not to determine whether it is accepted or not.
As for the actual mechanism used to signal, a number have been used in the past:
Time based: BIP16, BIP30
Early softforks (up to mid 2012) used a simple time based activation mechanism: node software that implements these proposals enforced the new rules on all blocks with a timestamp after a certain date. In the case of BIP16, this date was determined (and modified) in response to miner signalling, but this signalling was just for human interpretation; nodes took no automatic actions in response to it.
Specifically, the signalling used here was to put a string with a support message in the coinbase transaction's scriptSig field, which is otherwise free for miners to put anything in.
Block-version signalling: BIP34, BIP65, BIP66
A later generation of softforks used the block header's nVersion field for signalling (up to the year 2015). Each of those used a subsequent version numbers (BIP34 used version 2; BIP66 used version 3; BIP65 used version 4).
Whenever 750 out blocks number N-1000..N-1 (so 75%) had the proposal's version number of higher, block N would be subject to the proposal's rules. Whenever 950 out of blocks number N-1000..N-1 (so 95%) did, the next block would be required to also signal for it - resulting in a final lock-in.
Versionbits-based signalling: BIP68/112/113, BIP141/143/144, BIP91
The rollout of relative locktimes (BIP68/112/113) and Segregated Witness (BIP141/143/144) used a different mechanism, which had its own document, BIP9. It specifies using one specific bit of the block header's nVersion field for each proposal, and a finite state machine to determine when to signal and when to activate. Its purpose is/was to permit multiple concurrent proposals to activate, without needing to have one completed before the next one can roll out. This was a downside of the previous mechanism, as it would be impossible to activate the proposal with version 4 without also signalling for activation of the proposal with version 3.
Due to various reasons, segwit was not entirely uncontroversial, and eventual activation happened through a meta-proposal, BIP91. BIP91 itself used BIP9 to activate, which then on its turn made signalling for BIP141/143/144 mandatory, resulting in its activation in August 2017.
The future?
There are a variety of mechanisms available these days, and there is active discussion on what to use for the (likely) next softfork, specified in BIP340/341/342 (Taproot). This includes a variant of the BIP9 versionbits mechanism, called BIP8. An article on the various possible schemes can be found here.
Disclaimer: I am a (co-)author of several of the listed documents in this post (BIP9, BIP30, BIP66, BIP141/143/144, BIP340/341/342).