How to select features containing specific text string using an expression in QGIS

You just gotta use the LIKE operator.

For example, "TITLE" LIKE '%MINERAL CLAIM%'

The % symbol acts like a wildcard.

LIKE is case-sensitive, whereas ILIKE is not.

I had this exact problem and solved it from the python console with regex. While regex can be tricky it's very powerful. And you'll be left with a tool you can use with more difficult match cases. Here are the docs. and here is a nice online machine for testing your regex strings.

Firstly here is the quick script I run to check my regex strings in qgis

import re
RES_STRING='MINERAL CLAIM'
REGEX_HAYSTACK='DISTRICT LOT 5639, BEING AWARD NO. 2 MINERAL CLAIM, KDYD'

REGEX_STRING=re.compile(RES_STRING)
print "searching for "+RES_STRING+" in "+REGEX_HAYSTACK
REGEX_MATCH = REGEX_STRING.search(REGEX_HAYSTACK)
if REGEX_MATCH:
    print "found '"+REGEX_MATCH.group()+"'"
else:
    print "No match found"

Once you're happy with your regex matching you could wrap it up in a function to provide a selection for all the features that match. Below is a function to do just that.

def select_by_regex(input_layer,attribute_name,regex_string):
    import re
    RES_STRING=regex_string
    attribute_name_idx = input_layer.fieldNameIndex(attribute_name)
    if attribute_name_idx<0:
        raise valueError("cannot find attribute"+attribute_name)
    else:
        fids=[]
        for feature in input_layer.getFeatures():
            REGEX_HAYSTACK=feature[attribute_name_idx]
            REGEX_STRING=re.compile(RES_STRING)
            REGEX_MATCH = REGEX_STRING.search(REGEX_HAYSTACK)
            if REGEX_MATCH:
                fids.append(feature.id())
            else:
                pass
        input_layer.setSelectedFeatures(fids)


#USAGE BIT
input_layer = QgsVectorLayer('path/to/shape/file.shp','layer name', 'ogr')
QgsMapLayerRegistry.instance().addMapLayer(input_layer)   
regex_string='MINERAL CLAIM'
attribute_name='TITLE'
select_by_regex(input_layer,attribute_name,regex_string)

You will need to save this into a file and run it from the qgis python ide.

(untested but pretty confident)