How To Search Instagram via API Query?

First of all, and in case you didn't knew, there's already one similar (at least) web app. That being said, let's go to the answer:

You need to get your client_id, since you need it to call the API (More info here). You should be making calls to this endpoint (More info about Instagram's API endpoints here, you should read this :P):

https://api.instagram.com/v1/tags/SEARCH-TAG/media/recent?client_id=CLIENT-ID&callback=YOUR-CALLBACK

Of course, change the SEARCH-TAG with user input, CLIENT-ID with the one you got before and YOUR-CALLBACK with your callback function's name.

The response to this call comes in JSONP and looks like this (Taken from the API's page):

{    "data": [{        "type": "image",        "filter": "Earlybird",        "tags": ["snow"],        "comments": {            "data": [{                "created_time": "1296703540",                "text": "Snow",                "from": {                    "username": "emohatch",                    "username": "Dave",                    "id": "1242695"                },                "id": "26589964"            },            {                "created_time": "1296707889",                "text": "#snow",                "from": {                    "username": "emohatch",                    "username": "Emo Hatch",                    "id": "1242695"                },                "id": "26609649"            }],            "count": 3        }        "caption": {            "created_time": "1296703540",            "text": "#Snow",            "from": {                "username": "emohatch",                "id": "1242695"            },            "id": "26589964"        },        "likes": {            "count": 1,            "data": [{                "username": "mikeyk",                "full_name": "Mike Krieger",                "id": "4",                "profile_picture": "http://distillery.s3.amazonaws.com/profiles/profile_1242695_75sq_1293915800.jpg"            }]        },                "link": "http://instagr.am/p/BWl6P/",        "user": {            "username": "emohatch",            "profile_picture": "http://distillery.s3.amazonaws.com/profiles/profile_1242695_75sq_1293915800.jpg",            "id": "1242695",            "full_name": "Dave"        },        "created_time": "1296703536",        "images": {            "low_resolution": {                "url": "http://distillery.s3.amazonaws.com/media/2011/02/02/f9443f3443484c40b4792fa7c76214d5_6.jpg",                "width": 306,                "height": 306            },            "thumbnail": {                "url": "http://distillery.s3.amazonaws.com/media/2011/02/02/f9443f3443484c40b4792fa7c76214d5_5.jpg",                "width": 150,                "height": 150            },            "standard_resolution": {                "url": "http://distillery.s3.amazonaws.com/media/2011/02/02/f9443f3443484c40b4792fa7c76214d5_7.jpg",                "width": 612,                "height": 612            }        },        "id": "22699663",        "location": null    },    ...    ]}

Then you just need to process this response and do whatever you want with it :)

An important side note: instagram allows max 5000 queries for hour. This if you use the query with the app id.If you want to raise this limit, you can ask your users to authenticate. Then you can pass the the user access token.Hope this helps