Getting new work
I think that part of the issue here is that you are asking your colleagues to assign you work.
It is likely that your colleagues are busy with their own work and don't have the time to set aside to sort things out for you.
I'm assuming that there will be a team lead or that you will have a boss of some kind. I suggest you talk to them as your boss is supposed to aid in your time management and workload.
Let them know that you would like more work, or ask how you can help, what you can help with, failing that ask what you could be learning to make yourself more useful and desirable.
You are correct in thinking that it is bad to be sat around doing nothing, but in my experience there is usually always something to do.
If that work you occasionally get IS difficult then spend some time getting familiar with it. If you are allowed then revise it, learn it, get used to it's ins and outs so that the next issue that pops up you can deal with.
But at the end of the day it will always come back to needing more work, but you need to make sure you are asking the right people. Your boss, team lead or project manager are the right people to ask, assigning tasks, time management etc is usually part of their job, at least, where I work it is.
Failing that see if there are other project postings within your company, I don't know about you but we have an internal job board for projects that need more people to work on, you could always see if you have one of these and see if you are needed elsewhere, or see if you can find the opportunity to learn new skills on there too.
Of course, the above approach is only useful in the short run, once that job runs out you are back to square one.
So step two is to gain trust. Once you have demonstrated to your team that you know what you are doing and that you have the needed skills then they will begin to trust you more.
Once they trust you more they will be more comfortable with giving you important tasks for you to carry out, but until then you will need to be patient, gain skills, gain experience, even if this means self teaching yourself the complex system, and eventually the trust will grow.
But how do I grow trust?
Trust is a difficult thing to cultivate between team members, especially in high pace scenarios, but there can be a few good points to follow to try to gain this trust.
- Provide solutions
- Meet Deadlines
- Talk to your team
- Take an interest
What I mean by this is, attend the meetings, learn about the problems that your team are facing, think of solutions and share your ideas. If you can built a reputation as someone who is able to help find solutions then you will gain trust.
This one is more difficult as there are a lot of outside factors that affect this other than just yourself. Meet deadlines, getting a reputation as someone who is consistently delivering late is never good for your career.
Talk to your team & Take an interest
Sometimes just taking 5 minutes to talk with your team, get to know them better, meet up for lunch etc can help build external trust, those extra friendships help bridge the gap between co-worker and co-worker i would trust with an issue
Take an interest in their problems, see if you can help. No one likes being stuck on an issue.
However, remember boundaries. Don't consistently leave your desk, badger your team mates or appear to be avoiding work, this will build you the wrong kind of reputation.
When you have your issues and your jobs, work hard and appear responsible. No body would want to give an important task to someone who appears lazy and reckless.
I hope this helps you figure out a way to get more work through building trust in your team!