It really depends on the instrument. While there are many instruments that are fairly easy to "teach" yourself, in almost all cases it is good to have someone guide you in the learning process. There is so much information available on the internet for free, and with instruments like guitar it is easy to get started on your own - but even then you should seek advice from someone who plays. Most professional or even intermediate musicians will be able to give you some good tips just by watching and listening to you for a few minutes.
If you're looking to learn something like viola or trombone, you will almost definitely want to take lessons.
One great resource is undergraduate music students. They are generally desperate for income (I know from experience) and would probably be willing to take a few minutes to help you out.
These are two instruments that you can do a lot with on your own.
I learned to play guitar [mostly] on my own, with information I found on the internet. I would recommend that you pick up a decent acoustic guitar and google 'beginning guitar' and start from there. It's really helpful once you've piddled with it some to have someone else who plays decently listen to you. Guitar lessons are usually rather cheap, too, if you want to go that route. Even just a few lessons could really get you started.
Piano is a little more complicated. You can do a lot with a piano if you have a good ear and good coordination. For me, personally, piano is a struggle and has taken a lot more work/patience/practice. Most likely, if you want to play piano you'll definitely need lessons.
The good thing is that there are always a lot of people who play these two instruments, and a lot of them give lessons for reasonable prices.
Learning a musical instrument as long as you are willing to practice is easy. Really.
I would recommend against hiring a undergraduate music student. The may be economical option but these folks may have the "The Curse of Knowledge" as per the book Made To Stick. They will not have the patience to understand what it is like to learn something since it has been a long time since they were in the same shoes.
A seasoned teacher will understand where you are likely to get confused and need to really focus on to help you with the bumps and learn more quickly. They will have also reasonable expectations. This is along the same lines as Sir Ken Robinson stated in a TED presentation that college professors and TA are the worst teachers since everything came easy to them so they never fell into the same pitfalls that most students are stuck in. And so are unable to really help these students who initially struggle.
Hope that helps.
PS Pick someone who really enjoys the instrument. Yes there are teachers that hate the instrument they teach.
If you're looking to learn something like viola or trombone, you will almost definitely want to take lessons.
One great resource is undergraduate music students. They are generally desperate for income (I know from experience) and would probably be willing to take a few minutes to help you out.