Internet. You nobbut a youngster.
With most internet accounts you have a choice of ways of paying in. With Ing Direct for example (still good but not the market leader for interest they once were) you can:
Send a cheque through the post
Login to your account and arrange for the money to be 'pulled' from your normal bank account.
Login to your normal bank account (if you have internet banking) and 'push' the money to your Ing account
Call Ing and arrange things over the phone
You could also pay in over the counter at any bank, but the bank would charge you a fee to do this.
ICICI pay more than Ing and AFAIK operate similarly. They had teething problems when they first started but things seem to have settled down.
I'd put �3K in a mini cash ISA for starters though - National Savings have a good one. You should get around 5% tax free as opposed to 5% less tax in a normal high interest account.