There are plenty of referenced texts in this short guide. You will find chapters on how to conduct a quantitative questionnaire, and measure the likes of inter-rater/intra rater reliability etc. when piloting. See the last slide in particular for a list of helpful books that you may find in your university library.  

Pilot testing or study is conducted to see the validity, time taken to fill up the questions, common understanding and interpretation of the questions by different target population. Depending on the data collection method you adapt you can do through online, phone, email or face to face interviews. A face to face interview is mostly preferred because it gives opportunity for researcher to actually assess the respondents' behaviour and willingness to answer each questions. Before you do pilot testing, you should have draft structured questionnaire ready. 

Usually, the record is maintained related to problems and issues faced in relation to respondents' understanding and interpretation of questions and time taken to respond each questions.  Based on this findings, plan for actual data collection is developed. 

How to conduct pilot study in quantitative (research)?

Agreed that you can refer to many research method text books available in the market.  E.g. 1 of them is the following:

Sekaran, U. (2003). Research Methods for Business, 4th Edition. Danvers: John Wiley and Sons, 2003

Alternatively you can refer to this YouTube link to get some fast ideas how to conduct a quantitative pilot study:

https://www.youtube.com/results?search_query=how+to+conduct+pilot+study+in+quantitative+research

A pilot or preliminary study is referred to a small-scale of a complete survey or a pretest for a particular research instrument such as a questionnaire or interview guide (1). Pilot studies could be conducted in qualitative, quantitative, and even mixed methods research (2).

Pilot study

Saunders et al., (2007) state that prior to using the questionnaire to collect data it should be pilot tested. Saunders et al., (2007) point out the purpose of the pilot test is to refine the questionnaire so that the respondents will have no problems in answering the questions and also there will be no problems in recording the data

Fink (2003b) as cited in Saunders et al., (2007) state that the minimum number for a pilot study is 10.

Good Luck

Reference

Saunders, M.N., 2007. Research methods for business students, 5/e. Pearson Education India.

Following.

Excellent answers and references. Best regards

That is also my question. I will be checking in here for the snswers.