Two weeks ago, I started looking for a better job. I got a job offer from another company. They know that I am currently employed, and have to give 30 days notice.
Now they want me to start early in two weeks because it is urgent. They won't wait until the end of my notice period, but I really need that job and don't want to lose it.
How should I negotiate this situation?
I'm assuming that by "30 days render" you are referring to a 30 day notice period with your existing employer and that your new employer wants you to start earlier than this.
Depending upon your jurisdiction you may be legally obligated to fulfill your notice period if your existing employer requires it. This being the case all you can really do is talk to your existing employer about the situation and see if you can negotiate an earlier leaving date and if they won't budge on the date then you'll have to go back to the new company and explain that you cannot start until the end of your 30 day notice period.
As motosubatsu pointed out, it actually depends on your jurisdiction and terms of employment. You could check your earlier offer letter and see if there are any 'buy-out' option for the notice period. You could also speak to your current supervisor/HR and find out. You could ask the 2nd company to buy out.
In another approach, if the 2nd company wants you to ramp-up on any specific technology/skill, which they think will take 2 weeks and if you could do it independently, you could start on them so that you hit the road running (you have to ask the 2nd company if that is the case).
Otherwise, starting in parallel on both jobs, it would be difficult.
Negotiation is the best way forward here. The reason notice periods exist is to allow your current employer time to find replacement resource and for you to hand over any knowledge and tasks to someone else.
With a 30 day notice period, it's not uncommon that a company won't be able to recruit a replacement within that time anyway (since they may also have a similar notice period with their employer) so typically you end up handing over to an existing employee and/or documenting your work, which may not take up all of your notice period.
My point being that if you speak to your existing employer and can work out a deal where you hand over/document all the necessary information within two weeks, they may be happy to accept an earlier end date. After all it will save them two weeks of your wages, during which time you might not be doing much productive work anyway. This is definitely a conversation worth having.
Supposing they are reluctant to let you go any earlier then you really only have two options:
Think what you want to achieve. First, you don't want to end up without a job. Second, you want the job with the new company. Third, you don't want to get sued by the old company.
The rule is that you give notice when you have a signed contract with the new company. If you talk to your old company earlier (like "I have an offer from another company, would it be possible to leave with only two weeks notice"), there's the risk that the old company says "Don't worry about notice, you're fired" and then the new company says "we changed our mind and hired someone else". So you can't do that.
You can't sign a contract to start in two weeks if you need to give 30 days notice, because that means you can get sued by the old company. That's completely out of the question.
The only way you can start with the new company is if they offer you a job with a start date 30 days from now. In addition, you can agree to start earlier if you can reduce the notice period, so with this contract in hand you can give notice and ask for a shorter notice period, or the new company can call the old company and offer them cash to let you go earlier.
If they insist on a start date in the contract that is earlier than your notice period ends, then they are entirely unreasonable, and there is no way you can accept their job offer. One, because you will be in trouble, two because you don't want to start with a company that proves itself to be unreasonable before you even start.
