Ok, I'm sure this topic has been discussed many times, but here's how I solder such parts. You do need 'some' things, but a reflow oven/station isn't one of them
1) Pointed tip soldering iron. A chisel type tip *can* be used but it just makes life harder. A temperature controlled iron is great, but its not necessary (just let it get back up to heat between uses).
2) Thin solder wire. Thinner the better, 1mm is just too thick, 0.6mm or 0.7mm is widely available. (also, unless you're making this for industry, use lead solder - lead free has a higher melting point and just makes life *more* difficult).
3) Flux. Either the jelly kind, or 'flux pen'. I use a pen as you can 'paint' the pads with it.
4) Tweezers - to hold the little chip whilst you solder.
Generally, I start by putting a tiny blob of solder on one pad, say a corner pad. Then, pick up your chip with the tweezers, lay it on a flat surface (still gripping with tweezers) and gently press down on it (with a finger nail), so that when you lay it on the board holding it in the tweezers - it actually sits flat.
Lay it roughly into position, with one of its pins sitting over your soldered pad, and bring your iron to the edge of the pad, melting it, then press your chip down. It *should* solder to the pin, at least enough for holding the chip in place. If its wonky, or skew, you can re-heat the pad, and adjust the position of the chip. Doesn't have to be 'perfect', as long as the pads line up, and you have enough pad space at the end of each pin to get your iron on.
Now, you'll want to do the opposite corner, just to hold the chip firmly in place. Dab your flux on the pin on the opposite corner, heat the pin (not the chip! thus the fine tipped iron) and add solder wire until the pin is soldered to the pads.
Do not worry about solder bridges. We just want to get the chip into position and held there with solder via its pins. With two corners soldered (or multiple pins) you can proceed by cleaning it up. This is why flux is a godsend in such situations. Paint both sides of the chip (edges, on the pins and pads) in flux, add some solder to your iron - enough to tin it, with a tiny bit of excess, then lay your iron across one side. The flux should make all the pins on that side solder, and remove bridges. Do the same for the other side. So really, you're soldering all the pins on one side, in one go.
Any bridges (they happen all the time) can be removed by letting it cool, adding MORE flux to the pins/pads, and reheating with a *clean* soldering iron (clean meaning, tinned, but no excess solder). The flux will help the solder flow, and any excess forming bridges will be sucked onto the iron. You can repeat this step a few times, as long as you let the chip cool in between attempts. Place the iron across the pins and drag the iron away from the chip - horizontally. Not sideways, but away from the pins. Surface tension is your friend and will drag the bridges with the iron.
If you still can't get rid of the bridges, another method is to flood the whole side of the chip with solder. Forming one 'big' bridge where all the pins/pads that side are joined with solder. Then, just heat and use a solder sucker (desoldering tool)...OR if you have it... solder wick. The solder sucker will pretty much suck up all the excess solder, and because of surface tension, the excess will drag the bits of solder in between pins with it.
If you do not have solder wick, the copper braid shield found on many cables (USB, audio etc..) will do just as well. Either way, pre-bought wick, or copper braid, wipe it with flux first. Lay it across the pins (the whole side) and lay your iron on it to heat. You'll see the wick turn tin coloured as it soaks up all the excess and leave beautifully soldered pins with the perfect amount of solder on each
.
After all that you *should* have a very nicely soldered SMT chip, with some gooey flux residue around it - that can be cleaned with lighter fluid, acetone, some fluxes are even water soluble.
The above method, as complicated as it might seem, has allowed me to solder TQFP144's (0.4mm pitch), MSOP's, SC70's, SOIC etc..etc.. without much fuss. Although it might be seen as 'neater' to solder each pin individually, there's no real need - a row of pins can be done 'in bulk', and clean it up afterward. In fact, I regularly do SOP14's (0.5mm pitch) in one go. The flux helps the surface tension of the solder to 'glue on' to the pins/pads, and not bridge.
Apologies for the long explanation, I thought I'd add too much detail, rather than not enough. I reckon you could do it without tweezers - some just tape the chip in place, leaving one side open, solder than, then remove the tape - others use a paper clip
I'm sure if you search the forums, others have much better explanations/methods. Whilst MSOP isn't the easiest SMT part to start with, its certainly doable.
Good luck!!