You can show emotions/feelings via 'Atmosphere' as in Bram Stoker's 'Dracula',
via utilising other characters in the novel to distinguish/accentuate your own personality and reasoning skills as in Charles Dickens, 'David Copperfield'
via your reactions to the changing circumstances or responses to social conventions as in Charlotte Brontes 'Jane Eyre'
There are various methods you could employ to convey your emotions and thought processes without resorting to such bland statements as 'I'm sad'. If that is going to be the general attitude then you may as well write that 'this is a story were sometimes I am sad, others were I am happy and in the end I die.'
First Person provides you with a genuine MC account of how s/he experiences and reacts to what is happening. I find this incredibly enriching not only in so far as character development goes, but in driving the story.
Once you have fleshed out an intriguing MC then you can convey his/her emotions by relating to, as I have, to nature (bruised, solemn clouds; the mournful cries of crows or the dying embers of the sun) or to people (sardonic smile; flinched from the reflection of my emaciated visage). Because all that you write about is from the MC point of view then the connotations etc. will reflect the internal struggles of the MC.
Use all the five senses to your advantage:
If s/he is happy see the world in colour, if sad on the other hand then in black and white. Or if you wish to be inventive use contradicting notions such as 'burning snowflakes' to create an atmosphere. Externalise the emotions of the MC rather than simply state them.
Internal dialogue is crucial for such purposes and I believe that this has been previously covered. I use a lot of internal dialogue, but use this with a healthy balance of action. Attach something still/abstract (feeling) with something moving/concrete (action) to add substance to emotions and get your creative juices flowing as well as conjuring up vivid imagery so as to offer greater participation from the salivating reader.
I just hope that I am able to adhere to such guidelines strictly enough, and it is a very exciting endeavor.