Is it hard to budget when you only get paid once a month?
From personal experience, I don't think it is any harder to budget when you are paid once a month, as opposed to weekly or every other week.
What is harder is sticking to the budget, especially if you are used to getting a paycheck every week or two. During the transition stage, you tend to forget that there isn't another paycheck coming in a week.
My advice, which is worth what you are paying for it:
Gradually save up so that you have at least one month's take home pay in a savings account. This way, if you run short of funds at the end of the month, you can dip into your savings. First thing you do when you get paid is top off the savings. Slowly grow the amount in your emergency fund to three month's worth of take home pay.
Write down all your fixed costs--rent/mortage, insurance, car payment, student loans, utilities (usually you can work out an average cost per month), anything you pay every month. Add those up. That will show you how much money you have left for things like food and gas and fun things like new clothes and music and going to the movies.
Pay the fixed costs as soon as you get your paycheck every month. That way, you won't be scrambling to find money to pay the rent, or getting hit with late charges because you couldn't pay a bill on time.
Put money in your savings account after you pay the bills.
Then you know that what's left in the checking account is yours to spend as you please for the next 4 weeks. Do a little planning ahead--if you know you need to buy a friend a birthday present, or you want to go out with friends, mentally set aside that money.
I've been paid weekly, bi-weekly and monthly. I vastly prefer monthly, because I know how much money I have for the month and I don't have to wait for it. Getting paid weekly--I would want to pay a bill, but have to wait a week until a paycheck came in, which was a bit frustrating.
The one thing about monthly paychecks that I have noticed with some people is that they see something expensive they want and at the beginning of the month they have enough money to buy it, so they do. Leaving them with not enough money for food and gas at the end of the month. That's impulse spending, not a lack of budgeting. Once you have built up a safety cushion in savings, you can indulge in a tiny bit of impulse spending without running into trouble.