Many people do use Cytoscape, as Fereshteh mentions - it is quite good for constructing graphs and networks. I believe that it is now open source (?). Other pathway / network tools, like Ingenuity (commercial), are very comprehensive and professional, and really do a great job.
Another useful implementation, but in R, comes with the igraph package. It is a very broad package and has a lot of functionality. It takes a while to get into it (took me a week initiailly to really grasp it). The first step from an expression dataset to a graph object would be to create a correlation distance matrix and to coerce it to a graph adjacency object (see below).
QUESTION: I don't have a tutorial for this on Biostars but I will put one up if there is demand / interest (?). There are not many tutorials online about it.
graph.adjacency(as.matrix(as.dist(cor(t(MyData), method="pearson"))), mode="undirected", weighted=TRUE, diag=FALSE)
One can also use Euclidean distance
graph.adjacency(as.matrix(dist(MyData, method="Euclidean"))), mode="undirected", weighted=TRUE, diag=FALSE)
Then, by working through numerous (many) functions, you can produce very nice and weird graph objects that you will gaze at for a long time:
Just to add some complementary comments to the already great answers above. The term "Gene Regulatory Networks", is still a generic term, being part of the general concept of biological networks (which also includes for instance signaling pathways, metabolic networks), which still includes various categories, and numerous approaches for "network-reconstruction". Thus, which is your main goal for inferring gene regulatory networks ? For example:
1) You want to utilize your total expression set of RNA-Seq gene counts, define from this some "co-expressed" modules, and relate them to phenotypic traits or similar downstream analysis, such as functional enrichment ? To see their role in your phenotype pertubation ? Then in R, WGCNA is an excellent choise.
2) Or alternatively, wou would like mostly to infer co-regulatory networks ? That is, infer networks of interacting Transcriptional factors, that regulate a list of DE genes of interest ? and might play a crusial role in your biological system ? Then, CoRegNet R package is a wonderful choise, as it also has an option to use experimentally validated TF-gene interactions, PPIs, etc.
If still you are not interested in R, Cytoscape, Gephi or other standalone tools might be more easy to handle.
Also i would like to suggest a very interesting review about gene regulatory networks, and especially a specific sub-category of these, which is very popular: "gene co-expression networks"
https://academic.oup.com/bib/advance-article/doi/10.1093/bib/bbw139/2888441 (Gene co-expression analysis for functional classification and gene–disease predictions)