If you want to know what tissues a certain mRNA is expressed in, you can likely find plenty of RNASeq datasets publicly available. An easy starting point is http://www.proteinatlas.org where they have for each human gene the RNA Expression Overview based on their own RNASeq data, the GTEx project, and the FANTOM5 project. If you are working with a different species and can't find transcriptome datasets and really want to perform a microarray, the general protocol is to find a company or platform performing it as a service and to pay them. They will tell you what quantity and quality of RNA to send them.

Perhaps consider qRT-PCR if you have only a single mRNA of interest. It will be faster and cheaper.

You can use the GEO database (https://www.ncbi.nlm.nih.gov/geo/). GEO is a public functional genomics data repository supporting MIAME-compliant data submissions. Array- and sequence-based data are accepted. Tools are provided to help users query and download experiments and curated gene expression profiles.