Early on, you need to open a dialogue with persons relevant for your future career in Denmark. Your options to do so are many, even though they may not be obvious to you at this point. Here are af few starting points…

Student & alumni associations
A large number of student and alumni associations facilitate contact with business. If you join an association and participate in the work, you will learn about what Danish employers are looking for in future employees through your contacts with the companies.
DSE (an association of engineering students), is a good example. DSE is facilitating contact between industry and students and thereby offers different ways of getting in touch with Danish and foreign companies: career fairs, company presentations, jobbanks etc. And while several thousand engineering students profit from this work, you can also join approximately 100 students organizing the events. Through their contacts with industry, they learn a lot about the companies, and network. It is a brilliant way to make yourself known and test your ability to communicate with Danish employers.
A number of associations have similar profiles: sicef in marketing and business (Business students), Økonomisk forening, Juridisk Diskussionsklub (Law students) etc.

Social media offers a lot
Facebook, LinkedIn and other social media does not yet host large numbers of expat groups in Denmark. However, you will find a number of groups and associations, e.g. associations of students from China, Bangladesh or the US. Also you can find non-national associations as the European Law Students Association (ELSA) or International Veterinary Students Association (IVSA). And you can find generally accessible associations like AEISEC or ISIC. These associations may not all be focused on career issues. But they can nevertheless provide you with potentially  very helpful contacts. Consider starting your own group and  invite members to open a dialogue with potential co-workers or employers.

Your local contacts
Career centres, professors etc. at your university are perhaps some of the most effective contacts available to you. Your professors will often have both contacts to business and an eye on your academic skills. Their knowledge of your academic skills allows them to recommend you to companies without any prior evaluation by HR-departments etc. The career centre at your university or college can facilitate your contacts to industry as well and often has first hand knowledge of companies looking for specific skill sets..

Expat in Denmark
Expat in Denmark is a network for foreign professionals in Denmark. run by the Danish Ministry of Economics and Business Affairs and a consortium made up of the Danish Chamber of Commerce, The Copenhagen Post, and the Danish Bankers Association. Craig Till of Expat in Denmark explains:

Can all expats use Expat in Denmark?
Yes, there are quite a wide range of students, first jobbers, middle management, executives, spouses, service personnel, and everything in between, in our network.
 
Which benefits can an expat in Denmark draw from your organization?
Firstly, it’s the personal contact. ExpatInDenmark.com is an online portal, but most everything we do for our Expat members is “real-life”. It’s all about getting people to meet, socially and professionally, with other Expats or with Danes. Secondly, thay can attain information. We have built quite an extensive Infocentre with information on everything from schooling to how to exchange your foreign driver’s license, which is free and open to everyone. We have also collected a range of best practice articles, and other publications of relevance to the Expat community in Denmark which users can freely browse through.
 
What are in your experience the most common challenges facing expats in Denmark?
The two main challenges are the Danish language, and establishing social connections, especially with Danes. Some Expats also find it difficult to find a new job, and the extensive public sector can be a challenge – if you’re not used to it.
 
What is main benefit for expats working in Denmark?
The main benefit is perhaps the famous work-life balance. The salaries are fairly competitive, on a European scale, and even though cost of living is high, so is the quality of life. In particularly expats with children appreciate the focus on family time, and work flexibility.

Work in Denmark
Work in Denmark is one of a number of government programmes to attract international jobseekers to Denmark. The organization runs offices in Høje Taastrup south of Copentagen, in Odense and in
Århus. It also offers a jobsite in english and a number of links to information for jobseekers as well a hotline to answer any questions you might have concerning working in Denmark.

Your practical web-guide:
newtodenmark.dk
iu.dk/en
workindenmark.dk
studyindenmark.dk 
skat.dk/english 
laerdansk.dk/en
virk.dk/english 
jobbank.dk 
expatindenmark.com